Not sure if I'm being wooshed here.
He might just be overwhelmed with emotion or excitement.
Honestly, that's something you should be able to talk about.
Peace

In my opinion, the most important aspect of a healthy and strong relationship (romantic or platonic) is communication.

Talk to him. Mention it as an observation, ask him about why he thinks he does this, tell him your thoughts or concerns about it, whatever. It might be one conversation or multiple conversations over a period of time. The point is to bring up the topic and harbor a safe space to discuss anything with little to no judgement.

If it happens specifically when you hold his hand or hug him, it could be because he's neurodivergent in a way that makes those kinds of physical contact more difficult. As others have said, you can just talk to him about it. Just be open to whatever he says. Maybe he'll say "I want to hold your hand but every time I do it's really overwhelming for me". You'll have to accept him as he is if you want the relationship to succeed.

Can't vouch for your exact case, but I can tell you what works for mine.

One month is a short time to be in a romantic relationship, despite having known each other before. It may take time to settle in.

However, if you need to talk, then you should talk it out. It's important to be in the same page about the relationship. Otherwise it leads to tension.

I think the longer you keep the tension, the harder it becomes. While it's understand to not want to have awkward moments, some of these moments are unavoidable, and some are even essential. You may be afraid to risk your long friendship with him, but have it occur to you that you can use your friendship to your advantage in dealing with this awkwardness?

What you can probably do is intensify the touch in hope he get settled in more quickly. If you get some resistance, you can casually point it out to initiate that discussion in a light way.

I'm rooting on you!

Maybe ask him if he has contact aversion?

Some folks can just be extra sensitive to touch in certain ways and need time to adjust if they're in a situation where those touches become normal.

Most people touching me in a specific spot will make me actually jump out of my skin, it's like the feeling of a light but continuous shock, but the lady I be crushin' for is able to touch the same spot and it feels fine.

Probably he just needs time to acclimate, and if it's something more than that then there's no big deal there either.

If it happens, just say you're really excited this is happening.

That happened to me for the first little while with my first girlfriend, I was just nervous and excited.

I don’t want to ask him about this because I afraid he will get ashamed of this.

But the key to any good, strong, healthy relationship is comunication. All we can do is take our best guess as what's going on, you won't actually know though, until you talk to him. If you want this relationship to work, you(both) need to get comfortable communicating even when it's awkward or dificult.

Talk to him about it. Don't be confronting but do ask him about it.

Every relationship starts and ends with communication and trust.

Maybe tell him you've noticed and ask if there's anything you can do to help him or make it easier?

Yup, I agree. Tell him you noticed and ask why and if you can help. If you think he's just nervous I think it helps if you tell him how much you like touching him/how good he is to hold, that kind of thing. It might help build his confidence.

Can't answer question directly. Just, when I was your age, there was so much I needed to learn. Every person takes time to figure things out, overcome shortcomings, work thru stuff.

At 21, lot to figure out, discover, learn. For me, cuz childhood abuse, trauma, autism, I was a mess. No idea how to have healthy relationships, positive communication, etc.

So, could be your dude is just young, figuring stuff out. Or could be something else. Only way to know is to ask, talk about it. No assumptions, no judgment. Communication is key.

Might be useful to research how to communicate effectively. How to talk about stuff in not about criticize, instead seeing other person's viewpoint, meeting half way. Problem is, other person may not want to or be able to.

You're doing good, asking questions. Keep doing that, and good luck.

At some point he'll just get used to you touching him.

I don't see a reason to worry. You've probably seen in anime "oh no, she's touching me! I should act normal or I'll scare her". Of course that's just an exaggeration, but my best guess is that he's nervous because he likes you and don't wanna fuck It up.

First of all, make sure he's okay with it. But if you wanna speed up the process, just touch him more, let him touch you, etc. Again, only if he's comfortable, don't force him.

EDIT: just to make sure, I'll clarify, if he doesn't wanna get touched, touching him without asking will only make it worse, so it's probably better to go slower in that case (or not, ask him).