Yes...you need to drill some holes in the bottom of the party cups.

If it was me? I would let them go in the trays for now. Since you are going into cups (will one tray unit fit in a party cup?)

I would watch for the next week or so...and watch for roots coming through the bottom. Then I would cut one tray unit out and put it in ...whatever, it fits in...cup or otherwise. I have used 3 liter bottles; with the tops cut out and holes in the bottom.