If you’re spray-painting wood, you might need more than one coat.
You can use a wax-based furniture polish, as long as it’s in spray form.
If your finger doesn’t come away dry, let it sit for about 5 minutes. You’ll leave the furniture polish on the object permanently - it acts as a sealant. It shouldn’t create a film on your object, but it might look matte, rather than shiny.
Running a heater won’t necessarily reduce the dry time by a lot, but it should shave off a couple of hours (it normally takes spray paint about 24 hours to dry).
You can run a dehumidifier in the room where your paint is drying.
Make sure the room is clean before you turn the fan on. If there’s a lot of dust, dirt, or other debris in the room, the fan might kick it up and it can end up sticking in your paint.