Should I replace capacitors in an old but working amp?

Its easier to service out a functioning amp. Harder when they failed because the maintenance was not performed.

It is time to replace the capacitors, especially if you intend on keeping it running. I'm a fan of don't fix it if it ain't broke, but in your case, definitely replace the caps. 105C caps or higher temperature.

Replacing the electrolytic caps with film caps if they can fit in the space. 

If you recap do it in parts.
Section done, be very carefull if you replaced them correctly sometimes the cap you took out is in incorrect plus or minus on the pcb printing. Get one out place the new one back in exactly like the old electrolyte. Ignore if the pcb board printing is otherwise. 
Most of the time pcb boards where ready for production, but later on they made mistakes. Then they put in the electrolyte the right way but the drawing on the board was wrong.
OK I would go for example 100uF 25v to 105 degree types nichicon but the 100uF 63v types. The higher voltage the electrolyte can handle the lower the esr. 
Or place two 47uF/ 63v parallel even better. Lot of small value microfahrad to combine the original value ( decoupling)
Most of the time the coupling caps are still good, but when your in recapping I would replace them too, look for high performance types mkp.
So clean all contacts look for bad solder joints they will give noise later on. 
Clean potmeters clean every soldier joint even the existing ones, doll looking joint most of the times they are bad in sound quality it pays of to clean it very well.remove Flux with 96% alcohol.
Board for board check every board if your amp is still working well. Better to find the fluke now then to search in AL your done boards. 
Goodluck take your time don't rush

The value of any electrical component can sway over time. Focus on resistor upgrades as well. If chokes and transformers have values written on them then have them checked too.

The tonality may change in varying levels for every item that you swap. Try changing out resistors and caps of similar composition to retain as much of the amp's current tonality as possible. I know from experience.  

Just replace the electrolytic power supply caps first after 20 years.

Film, mica, and non electrolytic capacitors can last for “almost forever”and I would not replace them.

If the equipment sounds like new, it is not time to do any repairs.

I enjoyed that amp in the 90's!  It's well worth keeping (even though I didn't....).  Yes, replace the electrolytic capacitors after 20+ years in any amp.  I did that with a tube amp and it was a very nice improvement.
If you are handy with a soldering iron, you can do it yourself for low dollars (actually, you don't have to be that handy, because I was able to do it - - just get a good Weller variable control solder station and a good solder sucker, and you can tackle anything).  There are many great Panasonic electrolytics that are readily available from Mouser or Digikey, and they are rated for higher temps.
You will hear a bit of "sonic restoration", I'm guessing.

Absolutely. You have a 30 year amp, and it's' time.

But, modern caps last longer, and if you get higher temp variants they last even longer. So go ahead and replace them and you'll be good for 20 more.

The one downside is that you won't recoup this cost. If you have been on the shelf of trading it in or not you probably shouldn't.

I have an old Krell amp and I replace the caps. every 10 years and adjust the bias. I do that whether it needs it or not. I can't afford to buy new so I maintain what I have.