AIUI (but my specific unit is happy with breakers, so I have unfused disconnects.) Typically the labelling on the outdoor unit (and in the manual) will specify either:
- Max Overcurrent Protection Device (which is fuse or breaker)
or
- Max Fuse (which means you may have a breaker feeding the circuit, but the maker calls for a Fuse in the line.)
In the latter case you need the fused disconnect, with fuses of that size (or smaller, possibly, where "Min Circuit Ampacity" on the same label is a lot less than Max Fuse.) This has to due with the difference in how fast fuses and breaker respond to overloads, and how the unit was designed and tested. Some are fine with breaker curves, some need a faster disconnect in a fault condition.
The usual way you get 30 and 35A fuses in the same disconnect on a 30A breaker protected circuit is someone replaced one with the wrong fuse. It's not inconceivable for 35A to be the right size (since compressor starting can cause surges above the breaker rating, which a breaker will pass for a short period of time) but the way you know the right size and type of fuse is to consult the nameplate and/or manual for the device and check, not to guess.