I'm so on the fence about the whole cash/gift giving DW/AHR.
My husband and I moved in together almost 2 years ago, so while we had most everything we needed, I wasn't opposed to getting some new stuff to replace it! So we registered for a ton of stuff. I had a small shower beforehand with women who were invited to the DW and a few of my mom's friends who wanted to come (it was only about 12 ppl). I registered for that and got a ton of stuff from the registry, which was really nice.
We got married on St. Thomas in February and we are having/had 3 AHRs (one more left!!). If people who went to the DW gave us gifts or didn't give us gifts, I wouldn't have cared either way. However, everyone who went was our really close friends and we've gone to their weddings and stuff and they all reciprocated and gave us gifts! But for the AHRs, we started to feel like we were being greedy and having these parties for gifts. So in order to feel better, we actually wrote on the invitation "Your friendship is special to us, we ask that you bring no gifts." We ended up getting a TON of gifts, but we really wanted to put it out there that we weren't expecting anything from anyone.
IMHO if you want money, don't say anything at all and mostly not on the Invitation. I think it's severely tacky to write anything about gifts on your invitation. You aren't inviting people to a wedding to get gifts, you are inviting them to celebrate your love.
If you don't write anything, then people will probably give you cash, but if you specifically ask for cash, you will most likely offend people and they will buy you something you don't want and you'll be stuck with it!