+1. Even on our first trip to phuket when we were unprepared, the shuttle we booked at the airport was something like <$10 pp from HKT to Le meridien phuket beach resort. WE did have to briefly deal with the stop at some travel agency where they tried to sell us tours, which we refused with a smile.

OP's itin seems reasonable to me. We did a side trip to HKT from SIN a few years ago, 1 night at LM and 1 night sleeping on the beach at maya bay (just off phi phi). It was busy, OP's itin is far less so.