Superman can just fly through space, as could supergirl. Peronally I'd just drop the Sun thing and say they both came from a different Universe where the laws of physics are somewhat different, Krypton was of that Universe, and Superman has his super powers anywhere he travels in the OTU, unless he encounter's Kryptonite. Now lets lay those down as the groundrules for the purposes of a Superman/Traveller campaign.
The Story of origin goes something like this: Superman and Supergirl teamed up with Lex Luthor, or perhaps they were fighting one of Lex Luthor's minions. That Minion got out of control of Lex Luthor, maybe it was a demon, or robot or something, So Lex used one of his inventions to get rid of it, unfortunately that invention had a side effect of transporting the trio to a parallel Universe, specifically to Terra in the Solomani Rim. In the confusion, Lex Luthor made his escape, booked passage on a starship, stoled away or whatever, he has a pile of American dollars in his wallet, which turn out to be worth something to collectors on Terra, and with that he buys a ticket, perhaps moves to the Spinward Marches or whatever. Superman and Super girl will probably be unfamiliar characters in the OTU. Kryptonians don't need vac suits, they fly around as if they had reactionless drives built into them, and they don't even need jump drives, they can fly from star to star.
My question is, in the OTU, how fast can they fly through space? Apparently it was established in the comics that they can fly faster than the speed of light, so would you give them the equivalent of Jump 6 or maybe jump 7. With jump 7 its a parsec per day, and that makes the math quite simple.
Superman as a man-sized target in space is very hard to hit with a space ship weapon, just to be fair, I'd make him have to travel to 100 diameters before he can fly through space FTL, otherwise he accelerates just like a tiny spaceship (missile?) with a reactionless drive.
Superman is going to have a high AR, and after deducting that, he's going to have alot of Stamina points, and treat them as Strutural integrity points on the Starship scale. People are going to be quite amazed that such a small thing could be so hard to destroy, even nuclear weapons won't do him in, at least not unless they make a direct hit. Some people in the OTU might not be so pleased about some superpowered do-gooders flying around the OTU. Of course number one on their agenda would be catching up with Lex and perhaps getting him to build something that would take them back to their own universe, but in the meantime their would be plenty of challenges for them in Charted Space.