The rough rule I've read is 1hp per 500 lbs of displacement. My tartan 30 is 9000 lbs, from the factory had a 20hp diesel but was repowered to 15hp and reaches hull speed or close to it. With a 6hp you may struggle against a headwind or waves.
I owned a Catalina 27 and she carried a 9.9 Honda. I needed all of it at times with strong current in SF Bay. Wouldn't feel comfortable with less unless it was on a lake with no wind. No wind... Not a good thing for a sailor.
I've had good luck with the 6hp Tohatsu and high thrust prop in a well on my 8000 lb Triton but I mostly just go in and out of the slip/harbor. Once in a 30 knot headwind trying to get back to the slip against the tide in a narrow channel I felt under powered but was still doing 2.2 knots over the ground. Steep chop also slows the boat significantly.
Huge mistake! I have the same boat with a 15hp and the other day here in Oklahoma I was in 20+ winds from the stern when docking and it took everything it had to not hurt anything on the approach! I had a 6hp on my San Juan 7.7 and it couldn't control the boat during heavy winds. So unless you won't experience a variance of weather conditions it would be silly to go down any less.