Yes. Resolve If order matters, then resolve in turn order.
From Intrigue Rulebook:
Swindler - A player with no cards left in his Deck shuffles first; a player who still has no cards does not trash a card or gain a card. If the order matters (such as when piles are running low), resolve Swindler in turn order starting with the player to your left. Gained cards go to discard piles. If a player trashes a 0-cost card such as Copper, you may choose to give him Curse (if there are any left). You can give a player another copy of the same card he trashed. The gained cards have to be ones from the Supply, and you have to pick a card that's left if you can (you cannot pick an empty pile). If there are no cards in the Supply with the same cost as a given player's trashed card, no card is gained by that player. A player who Moats this does not reveal a card from his deck, and so neither trashes a card nor gains a card.
If in doubt or unable to determine
if turn order matters, I'd suggest using turn order.