I dunno how many red shards I have, but how many do you need for Ice Punch?
Should I go for Flygon then? I'm currently at the desert route. Can I get a Trapinch?
The elemental punches are the most expensive of the Red Shard Tutor's selection, you need 10 Red Shards for it.
I seemed to have plenty after exploring the Desert Resort and Route 4 with the Dowsing Machine.
You can catch Trapinch at the desert resort but it is rare, about 5% much like Eevee or Riolu.
They do become more commonly available when you travel to the next town after your 6th Gym Badge though, but if you don't want to wait that long for a flying pokémon, go to Desert Resort and find one.
I've heard there is an event Braviary/Mandibuzz that can be caught in Desert Resort on a certain day of the week.