DiMarzio Copper Shielding Tape  

... It will help. Doing it right means covering the entire control cavity, and making sure that the pickguard or backplate shielding makes contact with the cavity shielding in a few places. Also, if you shield a strat with tape but leave the 50s wiring entirely stock, you will still have noise. It is essential to wire with a common ground (google "star grounding" if you need more info) in order to fully kill the hum. Also note that if any of your solder joints contact the foil tape they can be shorted. I cover a few inside areas with masking tape for this reason. Used properly, metal tape will reduce noise without changing the sound in any other way. Other types of metal tape will work, but the stuff from Dimarzio and other guitar-oriented suppliers has a conductive backing meaning you don't need to solder to insure a continuous shield. I think that justifies the extra cost, YMMV.

my modulus bass came with a copper-lined back plate, so I got some copper tape (the kind that keeps snails out of your potted plants) and did the back plates of my gibsons. I got a slight (but worth it) increase in tonal quality.  (my new strat came with the pick  guard lined with what looks like aluminum foil, haven't tried the copper on that though).  you might just try the snail tape, which may be a bit thinner, which might matter some.

I have an American Strat with custom shop 69 pickups. I shielded the guitar following all instructions, soldering parts together, etc., and it substantially reduced the hum. HOWEVER, the brightness of pick ups was also reduced by about 20%, and I lost the bell-like sound that the Strats are for. So, it is your choice. Use rubber gloves during installation to avoid multiple finger cuts. If you want to do a good job on a Strat you would need two sets of these.