Change DNS for particular browser only?

I believe there is no other way but to use the hosts file. Check this addon can help you somehow SwitchHosts for Firefox.

There are several plugins for popular browsers that will allow you to make this change without editing system files. This is one of the fastest and easiest ways to check your server before pointing your domain.

All plugins require your desired host and your server IP to load it from. Each plugin will have different instructions to use. Instructions for proper use may differ based on version.

Here below are the plugins/addons I found (before installing, heck if they're still maintained and compatible with your browser's version).

Chrome

Virtual Hosts

Install Virtual Hosts

• Enter the fully qualified domain name in the VHost Domain field
• Enter the destination IP address in the VHost IP field
• Tick the enable check box

HostSwitch Plus

Install HostSwitch Plus

* Enter the destination IP address in the IP field * Specify the fully qualified domain name in the Domain field

Firefox

Switch Hosts

Install Switch Hosts

HostAdmin

Install HostAdmin