Hi Mike - I've not heard that tying the strap your way under the strings ever caused any damage to an instrument. An alternative, which doesn't involve screwing a strap button into the base of the neck, is to have a hook which fits under the soundhole - the strap goes from the strap button on the base of the guitar, over the shoulder, and then hooks into the soundhole.

I would personally get a strap button put in professionally - but I don't have a 40-year old Martin!