Several factors make this solvable:
You have a quick release basket, you have a wireless light,
and your basket is wire mesh.

So perhaps you could get some small zip-ties from the hardware store and strap your 'flashlight' light to the SIDE of your front basket, right along the top rim, facing forward, flush with the front corner? Since there are no wires on your light, you could simply leave it permanently strapped on the basket when you take your basket into the store with you.