I know Metroid Other M wasn't particularly well liked, but I've always thought the Metroid: Other M style of controls/foot gameplay would work pretty solidly for short Star Fox foot sections (without any first person stuff).
Make it so you can control multiple Star Fox members, maybe only one or two available the first time through, depending on the context of the mission, but when you replay a section you can pick any member of the team. Each one has different abilities so you can get some extra collectables or something. Make it so you can pick between a handful of weapons and subweapons. Make each level short and action packed, maybe like 1-20 minutes.
I just think the combat was pretty satisfying with the dodge mechanic. The boss fights were overall pretty good. It's simple and easy to pick up and that type of gameplay is ideal for Starfox out-of-ship sections.