Spit! All the direct-to-consumer ancestry kits do it with spit (you spit in a tube that has the chip at the bottom of it), so that's hard to do on the sly. You can do paternity/maternity comparison tests with hair if you're careful about what hair you get (you need hair with the root, trimmings from the ends aren't enough) and have samples from both the putative parent and the putative child, but those aren't the same as Ancestry or 23andMe where there's a whole database of people and you can get the whole family tree: it can only say "Mom can/can't be ruled out as the genetic parent of Zach" and not really quantify degree of relationship. (You also need all three samples: father, mother, and putative child -- to be accurate enough: with just two legs of the triangle, you can't actually distinguish parent-child from several other genetic relationships.)

Not that this is relevant to the advice! But yeah, in order to get an accurate genetic relationship, you need to either have all three points of the paternity triangle or have access to a very large database like the one Ancestry and 23andMe have built.