When you clip the nails make sure your nail clippers are very sharp so you get a clean cut of the nail tip. Dull clippers might leave a rough edge to still get caught.
You can trim the grooming nails if the are the ones getting caught - but just a very small amount from the very sharp tip. The grooming nails might not need to be trimmed every time you do the rest of the nails but if they are long and very sharp they could be the nails that are snagging.