I have a cheap Chinese Android TV box (H96 Max RK3528 - excellent for the price!), which allows me to install Vivaldi from Play Store. Vivaldi actually works very well on the device, with the obvious exception of no virtual mouse. However the device's remote allows you to emulate a virtual mouse using the remote's D-pad. It's a bit clunky, but it does work.
Another alternative if you have another Android phone or tablet is to install "Android TV ADB Mouse Keyboard" (from Play Store) onto that device, and then use ADB to connect the phone to the TV box. It lets you control the box's mouse and keyboard from your phone, and makes the whole experience much faster and sleeker. Totally free app, and highly recommended.
Aside from the mouse/keyboard issue, I've found Vivaldi to be excellent for playing web videos on the TV box. It's very fast and responsive, and video playback quality is superb. Since Vivaldi can sync to my desktop, that makes it easy to use bookmarks for web sites to play videos from. I've tried other browsers on the box, and Vivaldi is definitely the best.
I'd like to second the idea of implementing a virtual mouse option, similar to that in TVBro, BrowseHere, or Fire TV's Silk Bowser. The only other suggestion would be an option to have web videos automatically switch to full screen when played.
These features would make Vivaldi unique among mainstream browsers, and IMHO would make it a strong choice for a defalt browser for Android TV use. Ironically, even Google's Chrome browser has no support for Android TV devices...