British club bikes were transitioning from 26 x 1 1/4 (597mm) to 27 x 1 1/4 in the early and mid-1950s. After that, the performance bikes in Britain tended to be 27 x 1 1/4. That wheelset would be a good upgrade for a 1950s or later era club type bike. Selling the wheels and getting proper replacements is the way to go. The wheelset is relatively valuable.
I think I see the decal damage you mention. You still did OK. UPS destroyed an irreplaceable set of New Hudson celluloid fenders earlier this year on a bike that I bought. I'm not exactly optimistic with bike shipping these days between the cost and frequency of manhandling the boxes.
With parts, it's all on how much time and money you want to put into the bike. The brake calipers and levers can be located with time and money. They tend to be kind of expensive for what they really are (basic steel calipers and handles, but they're "Schwinn" after all). Original fenders will be kind of tricky because the rear would need to match the frame size, but doable with patience and money.
It's worth it, being a tall frame bike and somewhat of an unusual color. The only hesitation I would have with getting the parts is if there's damage to the frame. The seat mast should be checked for the miserable hairline cracks these frames sometimes form around the brazing at the seat stay to seat tube joint.