You can buy some of the larger syringes that have the needle that unscrews from the body of the syringe, pull the plunger out and fill them up from the back with your wetted priming compound and then reinsert the plunger while pointing the needle upward. If it's a large enough gauge needle, you can screw the needle back onto the assembly and use it to finely push the compound into the caps. I'd highly recommend to sand the needle dull before doing the above though. Definitely don't want to accidentally jab yourself with a toxic mix of priming compound.
This is somewhat how I do it, except I fill the syringe with duco cement and use it to place a small drop inside the cap before dumping the dry powder into it and tamping it into a hardened puck.