HT is about 12". DC Direct stuff is about 13". It would look poor. Your best best bet is just getting a HT Joker. Dunno what they sell for though so you might want to hold out for version 5,000.
It seems like some folks were using the DC Direct clothing on Hot Toys bodies back in the day, and they didn't look too bad. But yeah, with the stock DC Direct body, the head will seem very small. It could be modded to do so I'm sure, though it might require more work than you're willing to put into it. There have been several Hot Toys Jokers released. Three separate ones with the primary suit from the Dark Knight, two Bank Robbers, and one cop suit. You could probably pick up the first Hot Toys Joker for a pretty decent price if you keep your eyes peeled, which would have a superior body and better quality clothes (though possibly not more accurate) than the DC Direct one. However, you would want to get a sculpt from another Hot Toys Joker. Here is a V1 Joker:
Short answer is no. The Hot Toys Joker figures have the type of head sculpt with necks. DC Direct 13" figures are like normal action figures where the neck is part of the torso piece.