Thank you so much for the responses. With regard to the question of whether this is a wedding or not: We have not had a religious ceremony yet, which is what his family (and us) consider to be a wedding, so we view this as our wedding. We did the courthouse ceremony with minimal fanfare (i.e. just us and the JoP, no reception, no gifts) for very practical reasons. Some may not agree with this approach, but it is what it is. Plus, apparently European folks do that, so it can't be that wrong
I agree that mentioning gifts before the topic is brought up by others could be considered presumptuous, so I think we will use artk2002's wording to discourage gifts, if the topic comes up (unfortunately, in DH's culture, everything offered is expected to be rebuffed several times before being accepted, so that adds another layer of confusion). I also agree that failing to cash a check can be very rude and also mess with a person's finances, which was part of the discussion between DH and I.
To answer a question: DH's primary concern is about family members' financial situations. Several family members are coming from across the country and will incur significant cost to be a part of our ceremony. In addition, several may have some new financial problems, so we do not want to add additional burden.
Thank you all very much for your input.