I watched Star Trek because my dad introduced me to it. I'm now a dad and I am sharing it with my kids.
I don't know you, and I don't know your family, but if your father liked Star Trek enough to introduce you to it, my guess is that he wouldn't want his death to take that away from you. If anything, my bet would be he'd hope it would bring you comfort and fond memories and hope for the future.
I hope you can get there when enough time has passed, and I hope this message might help it all hurt a little less.