Yeah, it's not uncommon that the next higher voltage rating won't fit. In fact if you ever have to replace capacitors on a computer motherboard you may find that they have used capacitors smaller than you can easily purchase.
The 200V capacitor is almost certainly filtering the rectified mains. The capacitor is charged at 50/60/100/120 Hz (depending on the rectifier) and discharged at the SMPS frequency. This usually under less stress because the ripple currents are lower.
The problem with testing the capacitors with a DMM is that it will tell you the capacitance, which has almost certainly not changed a great deal. An ESR meter wil give you a quantifiable result that you can compare to the specs. For example a 11 ohms where the spec says 0.5.
The replacement capacitors should be low-ESR type capacitors (certainly anything filtering the low voltage DC). I've googled for the specs in some cases, but generally if it's a 105C rated capacitor it should be low-ESR (I'm not saying that all 105C capacitors are low-ESR, but if you see them, you should replace them with low-ESR). In consumer equipment it's a pretty reliable rule of thumb.
In general replacing an 85C capacitor with a 105C capacitor is cool. It's especially cool if the replacement is low-ESR -- it will probably run marginally cooler
There are possibly some places where the designer has relied on ESR for some reason, so it's not universal. I would be careful replacing large filter capacitors in some cases due to the possibility of increasing power-on transient current.
Rated tolerance for capacitors is huge. I wouldn't worry about it a lot in this application. It's highly unlikely to be critical.
Remember that the 200V capacitor can bite (in some cases quite badly). See if you can make out if it has some sort of bleed resistor. If not (and even if so), measure the voltage on it before you work on the board to see if it's hiding a special surprise for you or your equipment.
