small cable ties (neglible weight) which can be purchased at either an electrical supply store or an auto supply store should do the trick if any of the frame is visible from the outside (or attach to the compression straps - if any and the frame is not accessible. i'm sure you'll figure out how to best attach it). they come in all diff. sizes, but the smallest/lightest ones are all that you need. depending upon the length of your umbrella holster, somewhere b/t 2 to 4 should do the trick. they can also be used to "close off" one end of the cylindrical tubing you're using for a "holster" if it's open on both ends - 2 or 3 should do this nicely. you'll prob. end up buying a bag of 50-100 anyways, since they're sold in bulk.
no need to buy a spcl tool to tighten & cut the cable ties.
use needle nose pliers to tighten (can get tighter with the pliers than by hand). after wrapping the tie around the frame, through your umbrella holster, & through the cable tie's opening, pull it tight by hand. then grab the cable tie close to the where it exits its "pass-through" loop/opening. ROLL the needle nose pliers to tighten. this will cause the cable tie to wrap around the pliers as you ROLL. the plier handles allow you to exert quite a bit of torque. DON'T PULL the pliers - especially towards you. In a prev. life (i.e., ~25 yrs ago), when i was working as an electronics tech, a co-worker, who had been using needle nose pliers and pulling on the cable tie to tighten it, lost an eye when the cable tie broke & the pliers went into his eyeball. you can use nail clippers to CUT the cable tie. small cutting "*BEEP*" can also be used, but if yours are too large, you can get the cut much closer if you use nail clippers - no semi-pointed end left to poke/gouge/cut any light weight fabric or skin.