Itinerary for Dalmation Coast in May

We want to experience the area and are not that interested in lots of
touristy outings

and

Dubrovnik and stay for 2-3 nights

are conflicting statements

Dubrovnik is beautiful and worth seeing, but if you don't want touristy I would cut Dubrovnik to 1 or 2 nights tops.

If you want less touristy, then pick a less "popular" island than Hvar (maybe Mjlet, Brac, Vis, etc. or a park like Krka). I would keep Dubrovnik at 1-2 nights max - it's very small and overrun with tourists. Also, don't overlook Split and Trogir - part of exploring the area means taking in some cities and these are both very interesting. As far as wine tastings, there is the lovely Pelješac Peninsula (if you go there, then I'd suggest pairing it with Korcula and swapping out one of your islands). I'm not sure what you mean by touristy things - you've described activities that both tourists and locals partake of. Croatia is a very outdoorsy/nature oriented place and tourists and non-tourists take advantage of this by swimming, kayaking, hiking, sailing, etc.

Eight days is definitely not a lot so you'll have to make some choices on what to keep/cut.

We enjoyed Dubrovnik by checking the cruise boat schedule and picking days when few or no boats were in port, walking the city walls for a couple of hours late in the afternoon on one of those days so that it was not crowded, and taking some day tours outside of the walled city - 1/2 day afternoon evening bike tour with wine tasting (there were 4 of us tourists on that one) and a 1/2 morning kayak trip where we were the only tourists out on the water with our 1 guide. We also attended an evening "tourist concert" in a church with about 20 other people that we enjoyed immensely.

You should have a lovely time. You did not indicate when you will travel but many things close for the season in October. Even the islands (Hvar, Korcula, etc.) have smaller islands near them and you can rent a small boat for the day or be taken around. On Korcula, there are places to eat right along the water's edge and some have tanks of fish and you can select what you want for your meal. Try to get to Vis: it has vineyards, a small museum, a very nice restaurant and in the past, tours to the mountain cave hideout of Tito during his younger years.
Split has numerous sites - Diocletian's Palace, churches, outdoor markets where you can purchase lace and watch the people making it, and Split has high fashion shops that will remind you of Milan. Dubrovnik has several nice walking tours of the Old Town and your concierge or just about any place you go will have brochures. There are several wineries south of Dubrovnik and your concierge can help advise. If you go during the high season, the enormous cruise ships will dock in Dubrovnik and for the afternoon, fill the Old Town with tourists. But if you just continue with your own itinerary, you can enjoy the town when they leave around 4 pm. Get some gelato. Eat at one of the restaurants right on the water's edge. Walking the walls can take several hours, if you stop to take photos and rest. But is an essential part of the trip. Relax and enjoy the sea and sights.

In May, Hvar will not be at all busy. Providing you are not unlucky with the weather, it's a great time to visit, though the sea may be too cool for swimming for some. May in Dalmatia is when businesses that have been closed for the winter, tend to open again. The countryside is fresh and green, and those in the tourist industry are delighted to see new arrivals and have time to spend with them, unlike later in the year when they are rushed off their feet.