You can careen a fin keel boat. Just be extra careful. I would advise port and starboard legs as well as something on the stern. Boat Legs
You need to be extra careful with a fin keeled boat, though, and make sure the places where you attach the legs are very strong. Also, supporting the keel might be an issue on softer bottoms.
I don't think I would do this with my particular boat. Haida 26
but I am pretty confident that it is viable. Just riskier than with a long keel, or a boat with less draft.
I careened my previous boat, an Islander Bahama 24 with no ill effects, but it was a bombproof thick glass hull and a full keel with a keel hung rudder.
I talked to someone who had their Haida 26 actually fall off the stands in the yard, landing sideways, the hull was fine.
I agree, haulouts are a bit expensive when all you want to do is minor stuff.