I am mostly satisfied with this game's use of the Gamepad, as rarely as I use it. Outside of occasional amiibo battles and stage builder, I sometimes use it for light play remotely, mainly to maintain equipment inventory to keep it under the 3000 maximum. Most of the time I keep the Gamepad out of range of my console to avoid draining it, and I wish I could use my GameCube controllers for the Masterpieces demos.
Do you have the red, yellow, and white connectors from a prior console and an old working stereo and a VCR, regardless of whether it eats tapes? If so, you can hook it up to virtually any TV since the 1970s. When the N64 first came out in 1996, I was in your same predicament, with no TV newer than 1983. I resolved the situation by plugging the yellow wire into an old early 1980s VCR that ate tapes, and by plugging the red and white wires into a 1970s stereo unit via the phono jack, since it was too old to have the preferable AUX/CD jacks. Anytime I wanted to play my N64, I simply turned the TV to channel 3, turned the TV volume OFF to avoid hearing static, turned on the VCR, and turned on the stereo for the game's volume. I didn't mind the lack of a remote control for volume, as long as I could play.
You can do the same with the Wii U. Since you already have a picture, no VCR is needed. Just split off the red and white wires, and hook them into a stereo. In fact, old tube TVs are preferable because there is no input lag whatsoever for offline play.