You mentioned not wanting to change capacitors. I don't know of any models that meet that requirement. Not saying there aren't any, but I haven't come across them. Maybe some of the premium brands were consistent in using good caps, but I don't know.
The good news is that PSU circuit boards aren't nearly as hard to solder as motherboards are.
Probably my favorite of my PSUs is an Enermax EG465P-VE. archsan mentioned these up above along with the 365 which I assume is similar.
When I was shopping on eBay I noticed there are different versions of these PSUs with the same model numbers. The labels show different ratings and probably also a different ATX version compliance. Mine is v1.3, ratings are:
3.3v 35A
5v 35A
12v 33A
3.3v+5v max 200w
total max 460w
It straddles the transition from 5v to 12v oriented systems and so it seems able to handle anything (outside of modern behemoth systems). It even has a test point for measuring the 3.3v rail, something I've never seen on another PSU. 5v and 12v are already easy to measure using the molex connectors. For all these reasons it's my favorite test bench PSU, but I'd also use it in a build if I had another.
One thing that concerns me is that the fan is temperature controlled. There's a graph on the label showing speed vs temp, and I think it waits too long to ramp up the fan. PSUs with temp controlled fans do it for quietness reasons and so they end up letting themselves run hotter than they should IMO. But if it's not heavily loaded it's probably not an issue.
The PSUs I've used most frequently on older systems are the Fortron FSP300-60PFN. They're pretty common, sometimes you see that part number listed on PSUs from another brand but they're really the same PSU.
I bought a few of those on eBay several years ago. They are 3.3v+5v oriented:
3.3v 28A
5v 30A
12v 15A
3.3v+5v max 180W
total 300W
They work very well, I even used one on a late Barton Athlon system that had the 12v connector. That system was my main PC for a couple years with a decent load of cards and drives installed in it, and it's voltages were perfect throughout. Generally a 300W PSU like this was considered marginal for a system like I was running but it was totally solid.
Last I knew these were easy to find on eBay and relatively cheap, especially if you get them in bulk to save on shipping.
The problem with these PSUs is that they have cheap caps which you can presume are always going to be bad at this point. If you get one, recap it.
The above mentioned Enermax has cheap caps in it also. I haven't bothered to recap mine yet because I was lucky enough to find one that was still minty fresh (apparently unused), but before using it in a long term build I would need to recap it with quality caps to be safe.