What happens when we connect a metal wire between the 2 poles of a battery?

Yes Sam, there definitely is electric field reshaping in the wire. Strangely, it is not talked about in hardly any physics texts, but there are surface charge accumulations along the wire which maintain the electric field in the direction of the wire. (Note: it is a surface charge distribution since any extra charge on a conductor will reside on the surface.) It is the change in, or gradient of, the surface charge distribution on the wire that creates, and determines the direction of, the electric field within a wire or resistor.

For instance, the surface charge density on the wire near the negative terminal of the battery will be more negative than the surface charge density on the wire near the positive terminal. The surface charge density, as you go around the circuit, will change only slightly along a good conducting wire (Hence the gradient is small, and there is only a small electric field). Corners or bends in the wire will also cause surface charge accumulations that make the electrons flow around in the direction of the wire instead of flowing into a dead end. Resistors inserted into the circuit will have a more negative surface charge density on one side of the resistor as compared to the other side of the resistor. This larger gradient in surface charge distribution near the resistor causes the relatively larger electric field in the resistor (as compared to the wire). The direction of the gradients for all the aforementioned surface charge densities determine the direction of the electric fields.

This question is very fundamental, and is often misinterpreted or disregarded by people. We are all indoctrinated to just assume that a battery creates an electric field in the wire. However, when someone asks "how does the field get into the wire and how does the field know which way to go?" they are rarely given a straight answer.

A follow up question might be, "If nonzero surface charge accumulations are responsible for the size and direction of the electric field in a wire, why doesn't a normal circuit with a resistor exert an electric force on a nearby pith ball from all the built up charge in the circuit?" The answer is that it does exert a force, but the surface charge and force are so small for normal voltages and operating conditions that you don't notice it. If you hook up a 100,000V source to a resistor you would be able to measure the surface charge accumulation and the force it could exert.

Here's one more way to think about all this (excuse the length of this post, but there is so much confusion on this question it deserves appropriate detail). We all know there is an electric field in a wire connected to a battery. But the wire could be as long as desired, and so as far away from the battery terminals as desired. The charge on the battery terminals can't be directly and solely responsible for the size and direction of the electric field in the part of the wire miles away since the field would have died off and become too small there. (Yes, an infinite plane of charge, or other suitably exotic configurations, can create a field that does not decrease with distance, but we are not talking about anything like that.) If the charge near the terminals does not directly and solely determine the size and direction of the electric field in the part of the wire miles away, some other charge must be creating the field there (Yes, you can create an electric field with a changing magnetic field instead of a charge, but we can assume we have a steady current and non-varying magnetic field). The physical mechanism that creates the electric field in the part of the wire miles away is a small gradient of the nonzero surface charge distribution on the wire. And the direction of the gradient of that charge distribution is what determines the direction of the electric field there.

For a rare and absolutely beautiful description of how and why surface charge creates and shapes the electric field in a wire refer to the textbook: "Matter and Interactions: Volume 2 Electric and Magnetic Interactions" by Chabay and Sherwood, Chapter 18 "A Microscopic View of Electric Circuits" pg 631-640.

When the 2 electrodes are at different potential an electric field will be established. The electric charges will gather at the two poles. Positive charges at the cathode and negative charges at the anode. If the two electrodes are not connected by an external conductor they will not be able to leave the surface of the electrodes and they simply accumulate over there producing an open circuit voltage. As soon as the two electrodes are connected by a conductor the charges will flow by the forces of the electric field in the appropriate direction. If the connecting wire has no resistance or almost zero resistance then it will be a short circuit and a huge current will flow only limited by the internal resistance of the battery. If the electrodes are connected by a conductor through a resistance then the current will be limited according to the Ohm's law.

$I = \frac{V}{R+r}$ where $I$ is the Current, $V$ is the voltage between the electrodes, $R$ is the external resistance and $r$ is the internal resistance of the battery.

(Note: Electric field is not neutralized by the chemical reaction rather it is maintained by the reaction. No reshaping of the field takes place. The charges move through the conductor since it is the path of least resistance. It is similar to the flow of water through a pipe from a tank. The water flows since there exists a pressure difference. The flow of water does not depend upon the orientation of the pipe. it only depends on the pressure difference at the two ends. Gravitational field does not reshape itself through the pipe. Similarly no electric field reshaping takes place. Only the voltage difference matters between the two terminals.)

Additional comments for those who think electric field can reshape in a conductor along the conductor:

These are simply delta and star connected networks. Now if electric field could reshape then the lines of forces will intersect at three points for the delta and one point for the star networks. But we all know that lines of forces can not intersect. Hence no reshaping of field lines take place.