Yes, the best thing to do is to get as many bees off as possible before you start surgery on the comb.
Try giving them a little smoke, then with bee brush in hand, just gently brush them down onto the top of the remaining frames, back into the hive. You'll never bee 100% bee free, but with fewer bees in the area you need to work, it'll be less stressful for you. Then take your hive tool and slowly and gently (no abrupt movements here) work that burr comb off. I keep an old applesauce or mayo jar in my little 'kit' and put the burr comb in that.
I experienced a similar situation 2 days ago. I was up visiting my bees to split the hive and add a honey super. When I opened the hive it was VERY much in need of splitting - the bees were literally flowing over. I got the 3 boxes separated from each other and put covers over the boxes I wasn't working on, but the first box I needed to check, and the first frame (the very back one) I went to pull out was attached to the frame in front of it with capped honey. When I pulled it apart, the cappings came open and I had a frame with about a 4" diameter area of now uncapped honey and the corresponding frame next to it with sticky burr - what a mess. I put the open comb on the ground and covered it so I could work thru the rest of the box, but what a mess.
LONG story short, I did split the hive and get the honey super on, gave the girls the damage back to let them repair (with my apologies), and came away with only one sting.
One thing that I've found helpful, especially later in the summer when the hives grow and they have honey they're protecting, is plastic covers for the hives. You may have a time where you are checking a 2 or 3 deep hive or you're taking honey off and need to keep it covered. These are the covers I have, but you could very inexpensively make them yourself.http://www.beeworks.com/usacatalog/items/item139.htm