Usage of "nonetheless" and "nevertheless"
Solution 1:
The correct word to use in this situation is nonetheless, although it sounds somewhat awkward to my ear:
I want to talk to you nonetheless.
A more idiomatic alternative would be to use the word regardless:
I want to talk to you regardless.
I don't believe that nevertheless is idiomatic here. Nevertheless is usually used as a clause-initial adverb, and doesn't fall naturally at the end of a sentence.
Nevertheless, I want to talk to you.
Solution 2:
More common usage in British English would be:
No, I want to talk to you anyway.