Think more about presentation and different depths of the water than worrying too much about patterns. Like most people who enjoy tenkara, I also agree that presentation is more important than a pattern. I also do not fish one fly, simply because I like to tie different things and I would get bored tying only one pattern.
If you see fish rising, use dries and soft hackle wet flies. If its a creek, focus on drag free drifts, if it's a lake try landing the fly as delicate as possible, if that doesn't work try to entice the fish with some movement by skittering the fly across the surface. If you aren't getting any hits on the surface with the dries, try an emerger pattern or a soft hackle wet fly. Let your fly sink down, then slowly rise towards the surface... you'll probably get some strikes as the fly is ascending. If its a creek using this method, do short drifts and slowly rise towards the surface for your next cast, don't bring the fly out of the water too fast or you will miss out on some opportunities.
If you don't see anything rising to the surface, throw on some nymphs and go deep. Even if you don't see anything rising, throw on a terrestrial and give that a go. Alpine lake trout get a lot of their food from random things blown into the water. Scope out the surroundings too. Look for structure or where the wind is blowing. If you see a downed tree in the water, there's probably fish there. If wind is blowing the water in one direction, most of the food source will probably be in that corner of the lake and there will probably be fish there. You might be able to see fish circling a certain area and predict their movement into certain spots.
Ive never done it but you can try doing a dry and wet fly or nymph at the same time, fishing more than one part of the water column at once. Use flies that can multi task - a CDC & Elk or Elk Hair Caddis can be a Caddisfly, mayfly, or even a small grasshopper. A parachute ant could be mistaken as an ant or a mayfly. Killer Bugs (or similar patterns) could be mistaken for caddis larvae/pupa, crane fly larva, worms, or just something randomly delicious.
Whatever box you bring, you might as well fill it. Id rather come back from a trip with a bunch of unused flies rather than cut my fishing short because I only brought a handful.