I always wash my mouth with water after using it to minimise this risk.
Why not alcohol based hand sanitiser or working with methylated spirits.
I find it unlikely alcohol causes significant cancers from skin contact compared to running it through the body.
At minimum answering that question would help understand the risks.
[Edit] interesting claim -
"Alcohol may cause changes to cells in the mouth and throat that make it easier to absorb the cancer-causing chemicals in tobacco smoke"