Мне не нравилось, что приходилось это делать самому. ¿

Не хотел, чтобы было нужно... 🤔

Ну, можно сказать "чтобы пришлось"

Ну да, вы почти так и сказали

This basically means I wanted to avoid having to do it myself if somebody else could do it instead.

I think everyone understood the meaning. The problem was to interpret it because, не хотел, чтобы нужно/не хотел, чтобы пришлось sound really awkward. That's way I went with не нравилось, but I wasn't sure enough it would work there.

How about избежать?

Я хотел избежать делать это самому isn't very natural either. In real life, you'll say something along the lines of Я не хотел делать это сам. For some reasons, "have to" won't translate idiomatically there, at least, no one's come up with anything both close to the English and sonding natural.

Actually, your version in this last comment seems like the most natural. You should add it.

Хорошо)

I may be wrong, but for some reason it seems like the speakers hesitation might best be rendered by не хотелось