I think you have two issues here. One is that this senior staff member is undermining your confidence and possibly undermining your effectiveness at work, but it's difficult to challenge people over comments like this, especially when you're new in post and they're more senior than you. The other is that if he has noticed you're shy it seems unlikely that your self-assessment that you come off as "average" is a good reflection of how you actually come across (despite the effort you're putting in).
Generally speaking, if you can keep your line manager happy your job will be pretty safe, and the senior manager sounds like he's not challenging you to be less quiet, he just finds it unusual/discomforting/noteworthy. So fears that you may be fired if you haven't been formally told it's a problem are unlikely to come true. But it may harm chances of promotion in that office since he's likely to hold some sway. If you can't get past this with him, work on relationships with other senior staff so you have others who will fight your corner.
While I think the advice to assert your boundaries if he touches you is entirely reasonable (a good idea, even), it doesn't sound like that is the extent of the behaviour you find undermining, or even the main aspect. It's his repeating his opinion of you being quiet and making it the focus of his introduction to others that seems to be the bigger issue(?) If so, having a set introduction of your own (that you can practice in front of the mirror and become comfortable saying assertively, out loud) that contradicts his assertion may be one way to combat this. E.g. "I'm not actually quiet, just learning the ropes. I'm really looking forward to working with you." If you contradict him in a genuine and nice way each time he does it he's more likely to stop. You could also try challenging him directly (again, in a genuine and nice way) if you have the opportunity to have 1:1 time with him. Even a quick "I would appreciate it if you didn't keep calling me 'quiet' to other members of staff. It make sit harder to fit in." might make him reassess. Unless he's deliberately trying to undermine you, of course. If that's seems to be the case, look for another job asap, you don't want to be swimming uphill in your first post.
Alternatively, what's your line manager like? Can you ask them why the senior manager says it and tell them you find it undermining? Or is there a colleague you trust who may be able to alleviate your fears or suggest the best way to handle this senior manager?
You also need to think if being shy/quiet likely to be detrimental to your career more generally. You say you've been making a huge effort, but it seems you still come across as shy. There are roles where that doesn't really matter but probably more where it does, especially if you are career minded and want to be promoted. Do you need to work more on being outgoing at work? You can take classes in things like public speaking and networking that can help make it much easier to go through the motions at work even if it's not the way you'd act in your free time. If shyness is likely to harm your work prospects even if this senior manager wasn't in the picture, you might want to look into them.
Finally, just in case this becomes a bigger thing, I would start keeping a diary of all the incidents so you have something to refer back to should it end up being necessary.