I've done some research and unfortunately there currently isnt a method to run it on portables. The devs require the disc to help prevent hackers, and unfortunately a side effect of this is that we can't use any recent versions on our portables.
I think there is a way to install CT’s without ctgp but I’m not sure if it is easy to do the extra cups mod. (216 tracks total I think?) I’ll do some research and update this with what I find later.
Edit: yes, you can do this. Here are some video links. You will have to loosely follow them because they aren’t using Portablizemii but with some thinking it should be easy.
32 custom tracks of your choice (you can also change the music if you have a music pack you like):
Wiimmfi patching ISO/wbms files:
Edit 2: you can install more than 32 CT’s with “Wiimms Mario Kart Fun”
After scrolling down for a while in this link you’ll find a installation guide. Look for a install file from 2019 on the list of downloads and that should get you a ISO/Wbfs file with a bunch more CT‘s
Link:
http://wiki.tockdom.com/wiki/Wiimms_Mario_Kart:_Download_and_Install#How_To_.28English.29