That would certainly be a problem. For brick or stone, my spouse had drilled small holes in the mortar to secure the hanging nail, and as it is grey in color, it blends in on the off season no problem. I don't think that I would do that with my stucco as you would be altering the integrity of the stucco finish and might allow water to penetrate. I would suggest visiting the stucco vendor where it is purchased from and they may have fasteners available that may do the trick without harm.
1 year, 7 months ago