The Single Speed Shopper of Death™ and other shopping bike tales

Just a word of warning. Most early Shoppers are designed for 20 x 1 3/8" wheels which are quite a bit bigger than 20" BMX wheels such as Skyways. If you try to fit Skyways to one of these bikes, the brakes won't reach, even with long reach callipers. You need to look out for a late Shopper preferably from the 80s.

See here (20 x 1 3/8 in the fractional table and 20 x 1.5 - 20 x 2.125 in the decimal table)
http://sheldonbrown.com/tire-sizing.html

20 by 1 3/8 = 451
20 inch BMX = 406
So you would need a brake with a drop of about 23mm more than what was on the bike previously. There are units out there that go as deep as 95mm, so, no problem.