The H202 method would certainly work, but I was hesitant for fear of shorting and spending a week sans e-cig (GAH! 8-o)
I don't know what model it would be, but mine is a super-mini of the kind Blu sells. It looks very very close to the 401. This model has four holes around the atty and two at the tip around the LED. I've been angrily puffing on just the battery for a couple hours, dreading a trip to pick up a pack of analogues, when I read damitintrblagain's post.
I grabbed the two air holes at the tip to block them and sucked on the threaded end, I kept tightening until I could remove no more air. I tightened the pressure until my jaw began to tire, then quickly released my grip on the holes at the tip. I assume that this loosened whatever build-up had collected, or at least un-stuck the switch.
It draws well, maybe not like a fresh battery, but well enough to hold until I get one. I hope this helps.