There is a reason why new versions have been released and that was to cover a couple security flaws. So downgrading you will expose yourself to that threat of a hacker could get into your site which is not very nice.
I think rather then downgrade the core, fixing the newsletter to work with 2.3.5 is the way you want to go. What do you mean 'it doesn't work' do you get an error? It looks like newsletter hasn't been touched in a couple months so doesn't look like any ones fixed any recent bugs