For my collapsing cages for my rodents that don't bother the bungee cords, I use small bungee cords to secure the wheels.
My collapsible cages have 1/2" x 1/2" wire as they are sometimes used for mice. This means the bungee hooks won't actually fit through the wire.
This is a mini bungee purchased at Home Depot. Fold the bungee in half.
Slip the loop through the wire on one side of the wheel stand, over the wheel stand and back through the wire on the other side.
Slip the two ends through the loop.
Pull tight on the ends.
Always secure the ties high, preferably behind the wheel.
I need 4 bungees to secure the wheel. (When I use zip ties, I usually need 6 of those.)
Below is the wheel secured to the cage. Note there is no bungee on the lower "bend." My hamsters leave these alone, but no need to tempt fate. The bungees are pulled so tight, the wheel can be left unsecured on the lower bend.
The reason I like using the bungees over wire and zip ties for the collapsible cages is the zip ties have to be cut and tossed and the wire, I'm not particularly fond of twisting wire. I also don't like cutting wire and zip ties so close to the cage wire.
My preferred wheel is the Wodent Wheel, although my mice use the 6.5" Silent Spinners and flying saucers.