I’ve finally got my hands on a cheap soldering iron. It’s cordless and rechargeable, imagine that! I doubt it’s very good, but I guess it does the job for the few project I have.
In of those projects was replacing the battery on the motherboard that has the 486DX2-66.

That was quite easy. Sadly, it doesn’t work though. Maybe the soldering isn’t done properly. But it can also be that the battery doesn’t provide enough power. I will try to put the new battery on the motherboard with the 486DX-50. And look for another solution for the 486DX2-66.