There is no rep range for cutting. The same training that builds muscle in the presence of calories will preserve muscle in the absence of calories. There are pros and cons to high vs low reps for cutting, but I know from experience that I've built muscle with anything from 1RMs to 50-rep sets, and that same stimulus that tells the body that it's important to get more muscle if possible will also tell the body not to get rid of that same muscle if it can avoid it.
Higher reps burn more calories in the moment. If (pulling hypothetic numbers out of my posterior) a 1RM squat burns 5kcal, then a single squat at 50% 1RM should theoretically burn 2.5kcal, but can be repeated 20+ times, for a total of 50kcal or more.
Lower reps are a better insurance policy for getting all muscle fibres recruited. On a high rep set, the mind will likely fail before the body does. There are guys out there whom I can only assume are one half crazy and the other half insane, who use rest-pause methods to do 20 rep squats with their 10RMs. I think it's safe to say that they're getting a good dose of muscle fibre recruitment going on. Most people cannot push themselves to do that, however, so to rack up enough reps per set to really plough through their energy stores means the intensity may be so low that they don't actually push their muscles -- it's their heart and lungs and determination that burns out first.
A safe bet for the best of both worlds would be to work up to a heavy weight, and then strip the weight back and do some higher rep work. Incidentally, in my
Simple and Badass Fatloss Program from the stickies here, that's exactly what you do.
Of course, OP, the reason that your muscles are "soft and puffy" is because of the fat on top of them, not the muscles themselves, and the number 1 thing you need to do to get rid of this soft-and-puffiness is to get yourself into a calorie deficit.