This isn't about skin care but have found it helpful.

To avoid pulling on the eye area and stretching the skin: put your contact lens on your pinkie instead of your index finger. You need very little movement of the lids to insert it.

Found this out the day after I had my eye job and broke my glasses. I could worm the lens in without touching the lids.
I wear soft lenses.

It's also great if you have makeup on (esp mascara) and get something on your lens and have to remove it.)

Judy