They are much better off with you, than going to Petsmart. Who knows where they'd end up. I know you love them and are doing your best for them. Most people have had less than ideal set ups for their fish, found out later, and it's not always easy to fix it immediately. But you're taking good care of them, you'll keep an on eye on their barbels and keep their substrate clean I'm sure, so a couple of months on a smooth gravel until you can switch it to sand is far from a terrible home for them! They might end up far worse off and not nearly as loved if you gave them away. You're doing a good job with them so far and you clearly care a lot
Not a full recycle, no, you can just remove and replace the filter which will have most of your beneficial bacteria on it. But it's very likely that you'll have a bit of a mini cycle, since you'll lose all the beneficial bacteria that was on the gravel, and it'll take a few days to a week or so for the colony to grow back again to handle the same bioload as before. I just experienced this last week when I moved to sand, but used an established filter from another tank. Got low readings for nitrites, so needed to do 50% daily water changes for a few days to keep the ammonia and nitrites at zero. I was confused about it at the time and made a post
So once you switch, test the water daily, and be prepared to do daily water changes for a short time as the bacteria colonies re-grow. It's not like cycling from scratch, since you still have the type of bacteria you need, it'll just take a little time for the bacterial colony to re-grow enough to make up for the ones lost from the gravel. I think it took my tank four days to be fully cycled again, and nitrite levels were zero after a water change, and on the lowest reading when there were nitrites, so with water changes, it didn't get dangerous.
Were you planning to add more fish? If so, might be best to wait until after you've switched to sand, so the mini cycle isn't too bad. More stocking means more ammonia/nitrites/nitrates, so it's easier to ride out the mini cycle if the tank is lightly stocked, then gradually add your new fish in small groups later.