Q: If I decide to use Swap Plays For Draws, or Get On With It, and I draw Creepers during the execution of that option, can I ditch them immediately if conditions allow it?

…For example, in Stoner Fluxx, the Mooch can be given away to another player who has Weed, or Munchies can be trashed by “eating” any food Keeper on the table.

A: Unfortunately, no, you’re stuck with those. The Free Action associated with those New Rules is considered to be simultaneous with your turn ending immediately, which means that Creeper giveaways or discards which can only happen on your turn cannot be executed, even if conditions allow it.

Creepers with potentially immediate “on your turn” disposal include:

Shackles (Pirate Fluxx): On your turn, you can discard this along with one of your Booty Keepers in play (yes, it has to be yours).
Mooch (Stoner Fluxx: On your turn, you can give this away to another player who has Weed in play.
Munchies (Stoner Fluxx): On your turn, you can discard this by discarding ANY Food Keeper in play (yes, you can discard someone else’s Food).
Hangover (Drinking Fluxx): During your turn, you can give this away to anyone who has more Drink Keepers in play than you.
Party Foul (Drinking Fluxx): During your turn, you can discard this if you also discard one of your Drink Keepers in play (yes, it has to be yours).
The Master (Doctor Who Fluxx): During your turn, you can give this to anyone with the Doctor.
Dalek (Doctor Who Fluxx): During your turn, you can discard both this and any Doctor in play.
Weeping Angel (Doctor Who Fluxx): During your turn, you can give this to any player with the TARDIS.

Note that the following Creeper situations are instantaneous and do NOT depend on it being your turn:

Taxes (4.0 or Creeper Pack): If you have Money on the table, discard both that and this.
Drought (Eco/Nature Fluxx): Discard this if either Flood or Water is anywhere in play.
Zombie Repellent (Zombie Fluxx): This Keeper prevents you from ever having Zombies, deflecting them immediately away to another player.

There are several other Creepers which can only be discarded if you’ve had them since your last turn, or have them at the beginning of your turn, so this question will obviously not apply to those as well.