Washing hands after relations is a praiseworthy custom, not an absolute halachic requirement, but it really should be performed if saying shema and hamapil after relations. Having a washing cup full of water, a basin, and a towel in the bedroom can facilitate practice of this custom.

If one intends to go straight to sleep after relations, one should recite hamapil and shema beforehand, so they are not forgotten before going to sleep. (Even though the usual custom is to not to speak after hamapil, in this case you should not hesitate to communicate naturally with each other.)