You'd probably need an ESR meter so you might be able to check the caps while they are still in circuit

I had this dilemma with my LAPC-I.
It had something like 25 caps.

I ended up replacing all of them - took a few hours but the results were worth it.

yes, replacing all of them is always the best solution

I definitely do not recommend using an ESR meter while the caps are still on board. The ESR meter will drive a test signal (DC bias + AC) to the cap, so who knows how unpowered chips like it (most likely it will survive).

Any other things that are connected will mess up the readings (for instance there must be several capacitors between power rails, not just one, and other things too that draw current).

So you will have to remove a cap first before measuring to get any sensible results.

I would not blindly change every electrolytic cap on board, I'd try to figure out first why there is more noise on the other channel, like bad solder somewhere, and perhaps then why it is noisier than other cards.

Most likely the current capacitors are of same general purpose type, used all over on both power and signal paths, so feel free to do the same.

Do not expect too much from recapping. You might bring the noise level in balance on both channels but that is about it.
I had one of my SB Pro I's refurbished and it is hardly quieter than the other one.
I had much better results with combining these:

- changing the motherboard
- changing the PSU to an FSP ATX
- home-made EM Shielding aka "ghetto fix" Faraday cage for the card
- running stuff from virtual hard drive in DOS (zero HDD interference)
- rerouting the SB Pro's line out to the GUS line in with a cheap jack-to-jack cable with a volume dial. This seems to cancel out ~60% of static and hiss in itself...

Not a sound card per se, but I had an old Sega Gamegear with leaky caps that had really low sound output and hissing. Replacing the capacitors made a huge difference. If you can find the capacitors cheap on ebay or some supplier, it's definitely worth it, otherwise you can often find a donor PCB for caps from a broken VCR or something.

^ this is a common gamegear fault , it affects either sound or screen or both and it is indeed caused by the cheap caps used in it...