We said in a case that it is muttar!
For a Goy you are being Mattir a Chiyuv Missah and for a Yid, an Issur without a Chiyuv Missah!
Similarly, if a Melochoh has to be done on Shabbos, it is better to get a Katan to do it than a Gadol, (obviouxly in a situation that there is NO advantage using a Gadol) =No brainer.
I remember as a kid, my brother needed stitches removed on Shabbos. My father told me to bring the equipment from the Hatoloh guy’s house to ours! (Fun times, holding this box under my arm-Shinui!)