We've used Contours for our self-guided walking tours, but have not experienced Wales. In response to you question about doing it yourself with the aid of a luggage transfer company, my answer would be in two parts and dependent on questions you would need to answer:
First, how much work do you want to do or can you do in setting up the trip? I'm assuming that you want overnight accomodation with roofs and walls - inns, B&Bs etc. Depending on question two below, you will need to find and book sequention lodgeing within walking distances and your budget. Then you will have to coordiante luggage transfer with those locations. And you will have to be prepared for dealing with problems while you are on the walk.
Second, what kind of daily distances and hours can you or do you want to walk? If you can do longer mileage days, finding lodging options are easier than limiting walking days to shorter distances. Booking companies sometime need to provide and arrange for transfers between trail and available lodging to keep walking distances within you target range.
To use Contours trip options as an example of transfer:
The Twelve (12) walking days "strenuous/demanding" option requires two transfer days at the end of the walk: https://www.contours.co.uk/pembrokeshire-coast-path#PCP1
The Eighteen (18) walking days "moderate" option requires five transfer days to keep daily milage "moderate": https://www.contours.co.uk/pembrokeshire-coast-path#PCP5
You can self-test your booking capability by trying to find sequention lodging for the tour.