Have you spoke to the guy who did the work expressing your concerns and given him a chance to remedy in the manner you want?
Did you discuss solder joints with him before he started?
It's a little harsh to just refuse payment and get someone else in to remedy.
You're talking about someone's livelihood and by taking the hard stance depriving him/her of income without chance to rectify.
If they arrived promptly on the arranged date, cleaned up after themselves the only thing I can see they did wrong was not do the work as you expected. They kept their side of the contract and should be allowed to remedy.