Alright, there are several different answers that come to mind.
First and most importantly: Why are they asking to see the deck anyway? Yeah, there are some people who are just naturally like that. But these people are few and far between. I can't tell you the number of times I've seen someone say "Oh, he was just naturally intuitive" or something along those lines. And I try performing for them myself, and find that they asked to see their deck, but not mine. Truth is, if you think your spectator is just "like that", chances are, they're not, so think again, and think carefully: what are you doing?
Secondly, there are a lot of practical ways to deal with this. In no particular order, some general groupings would be:
a) Subtlety to prevent this from happening
b) Remove the gimmick
c) Switch the deck
d) Just show them the deck anyway
a) would include things like flashing the deck, handling the deck openly, starting with an effect which uses a normal deck and letting them examining it, etc.
b) would include things like palming a double backer out, etc
c) would include an in the open deck switch, the use of a deck shell, or even just putting your deck away immediately (but subtly!) after use
d) may sound counterintuitive, but you'd be surprised how easily a double backer etc goes unnoticed. The more hesitant you are, the harder they'll look. Often they don't really want to examine the deck - it's just their first reaction (refer to note one above).