I'm going to call this "slightly sexual", for clarity. I'll elaborate more on this later.
First of (this is mostly towards guys), if the attractiveness of the person really matters, then I would say it's probably sexual, and not platonic. I can play videogames with someone, or go out to eat with them, or go for a hike, and even if I think they are extremely ugly, that does not matter during this activities, nor am I thinking about that before these activities. A lot of this sort of therapeutic touch is about being mindful, correct? Well guys, be mindful of how you browse for cuddle partners. Where do your eyes land? Who do you end up choosing?
Now, there might be a lot of straight women who would say, "Attractiveness does not matter at all to me! I have cuddled with plenty of guys I was completely unattracted to." Perhaps you are looking for a feeling of safety, comfort, etc. Well, would you cuddle with a 6'5" 250lb MMA fighter&powerlifter woman? If so, then you passed - maybe it IS basically platonic. If not, then I would say it is sexual.
Now, it is very important to note that there is a difference between activities that are, let's say, "slightly sexual", and maybe you each genuinely have no desire to push things further, and say, physical flirtation that you each are hoping will end up in blatantly sexual activity. I think there is a lot of social/cultural resistance to "slightly sexual" sorts of activity, perhaps because there can be a slippery slope. But, I think it is disingenuous to label this "slightly sexual" as platonic, when what I have seen, from cuddle parties, browsing online, etc. is that it is slightly sexual.
I can almost imagine a future in which people are talking about how lips are like skin and need to be touched to, and so people sign up on a website for "platonic kissing" buddies. People would defend the label of "platonic" by saying kisses can be platonic, their aunt gives them a kiss and that is not sexual, etc. when would be different from browsing for a kissing buddy, a total stranger who you have no previous emotional connection or real relationship with, and then kissing for a long period of time (you wouldn't hire someone to pretend to be your aunt and then kiss you for a long time).
Anyway, I am not saying that cuddling is always slightly sexual, or sexual in any way. But I do think that the experience of browsing for a cuddle buddy online, and then cuddling with them, is almost always slightly sexual, and that is probably fine.