Well, look at it - when you have the 5-way switch in position 1 or 5, how far away from the body is it? you'll need approx 1.5mm for a pickguard (depends on what you buy). The switch on your guitar might be different to a DX.

Suggestions:

If you want to go ahead with fitting a pickguard, you could either cut a bit off the bottom of the plastic tip for the pickup selector switch (which will give you more clearance), or you could cut the slot for the switch wider in the pickguard so it doesn't get in the way. You could also buy and solder in a new 5-way switch - I've done this myself and it's pretty easy.

Or,

Make your own pickguard, and use thinner plastic.

Or,

You could sell your guitar, and buy the DX with a pickguard. ;)