Clear polyester film straps. Melinex 516, that is.
If the fan weighs a pound or less, four to six strategically-placed straps 1/8" wide should provide plenty of support. Perhaps one or two near the hub and several at the ends of the sticks. You might wish to use short pieces (1/4" to 1/2" long) of 1/8" diameter, clear or black plastic "aquarium" tubing to create stand-off spacers for the mounting points. You can run a strap through the tubing & pass both ends through one slot in the mount board; looks neat.
For that kind of item, multiple mounting points are needed -- not to handle the weight, but to give the item good overall support.