Ironically enough, one of the portions of the reception that couples tend to "dread" is the first dance (and believe me it's usually with good reason). Although, I think that the power of the love and the union overwrite everything else, I can totally relate to not wanting to do the awkward "two-step bounce" as onlookers watch for 5 incredibly long minutes. So, here's my advice:
Instead of deleting this portion of the formalities (it really is a memorable experience), why not try to spice it up? Instead of a waltz, sign up for professional dance lessons and try a foxtrot or even a tango! Not only will your guests be shocked (remember they were expecting the two step), but you will have designated on average 4 hours of time with your spouse during one of the most stressful times in your life, to do nothing but dance!
One of my favorite wedding moments was last October when I watched an amazing bride start her father daughter dance in the traditional manner and then hike up her ballroom skirt and break into a salsa that was to die for! When I say, everyone was on their feet, I mean EVERYONE (including the waiters) was on their feet and applauding out of control. It's your day, try a little something different. You never know, you just may be good at it!