I don't believe they check anything on the CV--it's mainly for them to just see what kind of work experience you have and what work you'd be eligible/looking for in the UK. You can show them job adverts looking for administrative roles or whatever to show the ECO that there's work out there you'd be eligible for, and that you're intending to work, but you can't count any sort of salary towards your budget unless you have a solid job offer in hand.
Honestly, I don't think a budget is a huge hassle, and I don't think it will annoy the ECO. Things the ECO could possibly get annoyed with is tons of online chat logs, tons of emails, things like that. The budget is a good way to show the ECO exactly what you're paying out, and helps highlight that 120 pounds a week left over you guys got--again, it's not *required*, but I don't think it'll send the ECO into a blind rage to have it included. If you feel comfortable including one, include one--it's your application, you shouldn't have to *hide* things from your fiance concerning it.
As for your bank statements, I don't *think* you have to include yours if you're not using them to meet maintenance requirements, or to bolster your finances any.