I can't believe you'd even consider this OP...
Don't you realize that all that sweet tube tone from the Mesa head will get digitized and lost when you pump it over wireless?? Do you know what uses wireless technology to transmit audio signals? BLUETOOTH!
What people don't understand is that computer mice, keyboards, kids iPads with Roblox installed on it, smartphones, and Playstation controllers ALSO use Bluetooth. I couldn't count on my hands and feet how many shows I've been to recently where some kid screwed everything up by watching Skibiddi Toilet YT videos with Bluetooth turned on. Consider yourself lucky if it's just that and not picking up Call of Duty voice chat via that Playstation controller.
Honestly, you could use 5.0ghz wireless, but get ready to lose a lot of power with its limited signal range. 2.4ghz is better, but very overcrowded (same issue as bluetooth), you'll be getting Joe Rogan Podcast audio or Chillwave youtube playlists going through your speakers.
If you want any hope of this coming out right, I'd use a modified Wii U controller (with the touchscreen) since it communicates using a different standard. What you'll need to do is jailbreak the console, run it in Wii emulation mode, gut a wireless Guitar Hero (or Rockband) controller, and put it in-line with your bass electronics. This is much easier if you have an active bass since it can feed off the 9v battery for power.
There should be a 1/4" to Wii U charger cable on AliExpress for around $49, but I'd actually get the OEM one on eBay for better signal integrity.