How to drain a baseboard radiator system for a repair? How to refill the system?
Why do you need to solder in the new pipe? 

There are pushfit and compression fittings designed for fix leaks. 

Assuming the leak is very small you could also use leak stop patty that you just form round the pipe

(Once you move away from solder, you may not need to drain the system if the leak is small enough.)