so I'm creating my own USB-A to USB-B cable using Canare mic cable, what do I do with the braided shielding?

Microphone cable may well have PVC insulation on the internal wires - not very suitable for high speed data which require low losses at 100MHz and well beyond... Data cables like USB, Ethernet usually have PE insulation on the twisted pairs. The problem is moisture, PVC can absorb a lot more than PE or PTFE, and moisure is lossy at these microwave frequencies (its why microwave ovens can heat food).
 
45+45=90 Ohms, which is not far off a typical cable, so it will probably work for short cables, but perhaps not for longer cables. I think that cheap USB cables are often not well matched so yours may not be much worse. The USB standard was created with practicality as the foremost consideration. But if you want a long USB connection, consider converter boxes for Cat-5 wire.
https://www.amazon.com/s?k=cat5+usb...7_13351709&tag=mh0b-20&ref=pd_sl_70lnlc00gs_e

https://electronics.stackexchange.c...hm-differential-impedance-and-single-ended-45