As someone else with contamination OCD (I'm a huge hand-washing person) I would say not cleaning the remote and washing your hands after touching the remote would be a pretty good way to start. If that is too much maybe you can start with touching the remote without cleaning, and then wait a designated amount of time before you can wash your hands?
It sounds like we have really similar types of OCD, so if you ever want to talk hit me up! I'd love to connect :)
Thank you so much!