Compare the new with the old. If values or bigger, not a problem. The tricky part is finding high capacity in that PSU size.
If you fit more W than is needed, it isn't a problem. If less or just the same Watts, can be issue.
Check all rails, some are not used on Amiga. So not important. Import one is +12V and +5V (+12V is used by drives as well, some drives are greedy here). -5V and -12V much less important, they are for things like serial port compatibility.
+5V is the crucial one, and like I said, you can fit more and greedier expansions than CBM thought was ever going to happen.
One thing that can cause an issue is the timer circuit. This came in as part of the PSU wiring. Big box Amigas can bypass with jumpers on the mainboard to set Powerline tick or NTSC/Pal tick. You don't have to have the signals coming in through the power connections, but if they don't, you have to set a jumper or two to get the board booting properly.
I hope you get some good usage of that A4000. I never owned one, I thought they were bit ahead of their time, like A3000, only more so. I did own an A3000 for a few years, and somebody else blew up the PSU one day while programming a Pacman clone in AMOS (he was a Pacman fanatic from childhood).
The gentleman sourced everything, did all the work, I just had to figure out the jumpers to get it booting nicely and the matter was resolved. We never did discover the exact cause of PSU failure. Probably old age, or vibration caused by excessive thrash metal music and similar. The main voltage regulators were shot to bits internally, all connections were fine. Just stock 25MHz A3000, no cards in it.