The qualities that are most vital are being good at consent, being good at staying emotionally present, and not radiating need. Consent is vital because any touch needs to be consensual and a cuddler needs to know how to navigate that and give someone safety. Being emotionally present and aware is necessary because that is the building block for being able to give cuddles that are emotionally nourishing as well as physically pleasant. Not being full of need is necessary because even if you are otherwise perfect, if you have great need you may unintentionally drain people with your presence unless they know how to guard against that, or you are amazingly good at putting it in a box for a time. (for people who are full of need, guess what would be great for them? a professional cuddler!)
A professional cuddler needs to be:
1) good at consent: good at noticing non-verbal "no"s and asking clarifying, specific questions such as, "is there any part of your body that you would like me to avoid touching? Is there any particular kind of touch that you do not like?" and things like "would you like to be spooned? would you like me to stroke your arms? do you want me to play with your hair?"
2) not touch-starved or affection-hungry. If they go into a session without their own tanks full, it is quite possible that their touch will drain the client rather than nourish them.
3) good at boundaries. They need to be able to state their own comfort level and to be willing and able to say no and perhaps end the session if the client is not listening to those statements and honoring them.
4) calm, with settled energy about them, so that the cuddles they give will be relaxing and they won't transfer any stress to the client.
5) comfortable with other people's emotions, able to listen, care, and hold space without getting swept along.
6) good at separating sexual touch from affectionate touch, so that they can both offer touch with no sexual energy and they can read when a client is not being platonic and set boundaries accordingly.
7) good at paying attention and good at reading people's reactions, so that they can tell how to adjust their touch according to what would be the most nourishing for the client.
8) very comfortable with cuddling, so that they don't feel self-conscious and make their client feel awkward and uncomfortable about receiving their touch. They need to have a level of confidence and willingness to change something that is not working for the client.
Only the last one is really about physical aspects. The rest is all mental! Not all of it is stuff you can control -- obviously people don't have a lot of control over how much they need or how calm they are or even how emotionally present they are (some disabilities can break you out of being present no matter how hard you try). Some of this is skill, and some of it is just qualities that you might have or you might not, and some is a combination.