1) Patching the tube will be an exercise in frustration. It is normal to put a one inch patch over a small hole so the distance from the edge of the patch to the hole is almost a 1/2 inch.
In your case, the distance from the edge of the patch to the hole will be less than 2 mm. Getting a good bond, that close to the valve stem will be difficult if not impossible.

2) If you don't like slime filled tubes, then throw that spare away. No point in frustrating yourself.

Living where I do, tubes are cheap and easy to get so I am a wasteful North American.