Don't worry, your question is fine, because what works for a CB antenna works just as well for a 10m antenna.
Yes, you could certainly substitute radials for the car roof. The general rule for radials laid along the ground is that they should be at least 1/4λ long. That's 1/4λ electrically; RF current flows more slowly through a radial than through vacuum or air, so the wires don't need to be as long. If the radials are laid along the ground, having the radials be a little longer than 1/4λ is no big deal. Material? Copper or aluminum is best electrically; most people use copper wire. Stranded or solid? There isn't much difference. Wire diameter? Thicker is better; 14 AWG would be deluxe, a bit thinner is probably OK. Insulated or not? Doesn't make much of a difference. How many radials? More is better; I'd say use at least four.
If you plan to elevate the radials, then things change. Then it becomes more important that the radials be as close as possible to 1/4λ long, because the radials aren't just returning current absorbed by the ground any more (that's an oversimplification BTW, but somewhat useful conceptually); elevated radials radiate RF because they are part of the antenna. Do make sure that elevated radials are where people and animals can't touch them.
As I mentioned, elevated radials are ideally 1/4λ long, which works out to be about 2.62 m long for US channel 19 and a 95% velocity factor. That's 8' 7" in imperial units. When a CB antenna is mounted on the roof of a car, very few cars have round roofs that are 5.24 m (17' 2") in diameter. So a mobile antenna already has some tuning circuit designed to compensate for a ground plane less than 1/2λ in diameter. So how long should your radials actually be? That's hard to say without knowing a lot more about the construction of your antenna and exactly how you want to use it.
I'd recommend experimentation. Start with long radials, and then trim them for the best SWR. When I say "trim", you don't actually have to cut the radials; if you fold the wire so the short end lays next to the long end, then electrically the short piece of wire will be part of the long piece of wire, as if you had cut the wire where you folded it. That way if you want to try a different length, you can just unfold the wire and fold it somewhere else. You can experiment with the length, and if the radials are elevated then you can experiment with their angle also.
If you're going to all the trouble of creating a radial system, if I were you I'd just cut one more 1/4λ radial and put it inside a piece of PVC pipe pointing up in the middle of the radials in place of the mobile antenna. (You'd have to experiment a bit with its length also.) Connect the vertical wire to the center of the coax rather than the shield. Then you would have homebrewed the entire antenna for not very much money, and you could save the mobile antenna for a vehicle.
If you do homebrew a radial system or an entire antenna, please come back here and answer your own question with the details of what you did, to help others.