Can I switch two pawns that are right next to the safe zone?
Yes, you can switch them (the opponent's pawn is not yet safe; see rules below).

And what the opponent then "can do" doesn't change. The opponent plays from that position as normal. Clockwise, as normal. If they can back up a few spaces (e.g., with a 4, see rules quote below), then they would find that helpful. Or switch back with you with another 11. Or similar. Otherwise, that pawn is faced with going around clockwise again.

Rules:

You may target that pawn with your 11:


  You may only use 11 for pawns in play on the open track — not
  at START, HOME or in a SAFETY ZONE.


and they can move backward from there:


  However, you may pass the entry space on a backward
  move (4 or 10 card) or as the result of a “SORRY!”
  or “switch” (11) card played against you.