I think you should absolutely do whatever you feel happy with.
FWIW, since you're asking about shy people and weddings, my view is that the wedding party makes a huge difference. The best weddings I've been to have been ones where there is a person/people in the wedding party who are taking charge of things so the bride and groom can relax. At one wedding, one of the wedding party quietly told all of us that that the brides were a bit shy about doing a full first dance, so could we all join in after the first verse of their first song - and we did, and the bridal couple didn't have to worry about it. At another, the matron of honour did this thing where she gave her speech, then stayed standing and chatted to the groom about how lovely his wife was, and that segued into the groom's speech - and that was what he needed to get the confidence to talk because he is very shy.
When I got married I was quite shy, and I thought I'd asked my family members to do quite normal things (eg., being ushers), and on the day they all just calmly didn't bother - it really floored me. I remember being outside the church with a photographer asking if we could take some pictures, and my brothers who'd agreed to show the guests to the reception venue (a few hundred yards away) simply grinned and shrugged and said they would rather I did that. I did step up, but my memory of my wedding day is me constantly nerving myself up to do things like calling to people to come to the reception venue, or clinking a glass to announce someone would speak, or whatever. It made me feel so much more on edge and nervous.
I would say that, if you have the sort of family/friends who can be relied upon, if you wanted to, you could have any sort of wedding so long as you prepared them to work around what you'd like most. And it might be lovely. If you are at all unsure about that, then I'd say have the most private wedding you can - and that will be absolutely lovely too!