You can use hydrogen peroxide, or pure alcohol like vodka or iodine.
No danger using any one of those on your finger.
I would still try a needle first, and keep scalpels for the second try, if needle experiment fails.
The larger injury you make, the longer it is gone take to heal.
Your problem may be Dyshidrotic Eczema, in what case killing bacteria may not have any lasting effect, as Dyshidrotic Eczema is actually triggered by an intolerance or an allergic reaction.