Yep, you can do it on DL.
As far as hotels, don't you want to stay where the wedding party is staying? Where are they staying?
I like the Hyatt too, but you have no status there. If the wedding party is in Waikiki, there are several decent Sheraton's, and a really nice W that several FT members have reported about in the Starwood forum. There's also the Hilton Hawaiian Village, which, personally, I didn't care for, though the Ali'i tower is very nice .. it's a separate 5-star hotel within the Hawaiian Village. Others seem to like it more than I did, so take it for what it's worth. I thought the property itself was very nice, but the standard rooms they gave us in the Rainbow tower were very plain. We expected more.
Most Waikiki hotels have view rooms with balconies. I think those rooms are worth the extra $$ or points it takes to get them.
I agree that you really don't need a car for your entire stay if you stay in Waikiki. If you go and explore the rest of the island (highly recommended), you can just rent a car for the day. Many of the hotels have car rental facilities right in the hotels. Hertz will not be far from your hotel, if it isn't in the hotel you choose.
A suggestion .. if the wedding is just a few days of your time, you might want to go somewhere besides Waikiki, perhaps to one of the other islands for a few days if you have the time. There are superb properties, both Hilton and Starwood (Luxury Collection hotels) on the other islands you might enjoy. If you island hop, search the forums for "interisland coupons", or you can check your programs to see if any of them have stellar deals on interisland coupons.
If you have some flexibility on where you stay, you can read up on the Sheraton and W Waikiki properties on the Starwood forum and on the Hilton Hawaiian Village on the Hilton forum.
-David