Having experienced torn ligaments on my L thumb, I can advise letting it heal. Do not use it if you can avoid it, especially cycling, as braking and shifting will make you use the finger and you don't want that.
Note that hand injuries, should you ever need therapy, are typically not covered under most medical insurance policies, which consider them "occupational therapy" (I.E. Workers Comp cases). Thus you end up with a lot of out of pocket getting your finger back and working.
And you need your index finger to work correctly. If you don't believe me, try typing a reply one handed.