I used an instead cup some of my inseminations (and a cervical cap with stem others). Don't know which time did the trick. I put preseed inside the cup along with sperm -- don't put too much in though, because I did get a bit of spill when I put too much. Just inserted it carefully and went about my business.
As for the contract signing... I think the donor has an argument. It honestly depends on the laws in your particular state (or country). It is true that the donor signing a contract could be used in court to prove that he was the "father" this could give recipients grounds to sue for child support (US laws). Depending on the state, the contract might hold as valid, or might be considered irrelevant. You should consult an attorney who specializes in these issues to see what would best protect your interests. In my state, it doesn't matter whether I have the contract or not, but both the donor and my husband and I were more comfortable having one. In another situation, I might feel differently.
These are important legal issues to look into BEFORE you conceive, so I'm so glad you brought up the subject.