I haven't tried carrying my n/s Hamilton totes without the lock yet, but I did experiment with taking off the lock and expanding the bag. When I took off the lock and unhooked the belt, I just replaced the lock on the bare hook and then pulled the bag open as far as I could. If I ever need to carry it this way, I most certainly will be carrying it by the short handles as a tote. Therefore, I tried nesting the loose belt ends under the upright short handles and the short handles seemed to hold the loose belt ends in place pretty well.
I would suggest getting a replacement key if you can. You can call MK directly for a replacement if your bag is still in warranty. I've already ordered extra locks for both of my n/s Hamilton totes, one in gold and one in silver.