Can I safely charge my laptop with a non-standard, third-party charger?

It depends. If the charger is compatible then the answer is "yes", if it's not then the answer is "no".

Chargers can be different in a number of ways:

• The size and shape of the connector on the laptop.
• If they are the same size & shape then the polarity of the tip might be reversed.
• Most importantly the voltage and current they supply might be different.

If all of these are the same then you might be OK. If not (especially the last) you might end up with a dead laptop. Though as Robert points out if the charger provides higher current you can use it. With one that supplies lower current it will be the charger that blows up rather than your laptop.

With recent developments in uniform chargers for phones and tablets, it's likely that laptop chargers have become more uniform in recent years too.

Take a look at what voltage they supply, the voltage shall be the same.

And then check polarity on the connector, i.e. positive pole in the middle.

And lastly is it big enough, how many ampere do they delivere?

All this is usally printed on the power supply or on the computer it self, and if the above seems ok then you can try at your own risk.