It is pretty typical to open gifts in front of guests at any sort of baby shower.
The purpose of them is to shower the guest of honor with gifts. They want to see your face when you open them. It's just the tradition. If you don't want to open presents around people make sure to have lots of activities and games because gift opening will be something that guests are expecting.
So you'll want to keep them busy.
There are however instances where you will want to skip this. This really depends on the type of person mommy-to-be is.
Our best advice.
If it makes you feel totally uncomfortable, DON'T DO IT! It's YOUR day. You can ask people to do clear wrap, or claim you want to be "eco friendly" and ask people to skip paper. When your guests arrive, meet them at the door, accept the gift/open the card, ooh and ahh and have one of your friends note the gift/giver and arrange them all to make a pretty display table.
You can take this even further; have the guests play a game while your opening presents, so that way your not the full center of attention. Not a game that needs everyone's attention, but can keep a couple people busy at a time. This way you won't feel awkward, with everyone just staring at you while you open presents. In toehr words, you can only say "awww" or "so cute!" or "I love it" so many times before it gets old.
So if you motto is: "I hate being the center of attention!"
At one shower we attended guests filled out their own bingo cards with what they thought the mother to be got and would mark them as she opened presents. It definitely steered some of the attention off mom since everyone was focusing on the game too.
Another way to get around it is have them bring the gift unwrapped. Then just have a display table. I've seen it done at bridal showers, but there's always some that are wrapped anyways.
Typically they want to watch you open up the gifts. At one baby shower one guest was hating on all the games we were planning and kept asking when we would just open the presents already.