Screwing it in,
OK then… Thing is, usually when you snap a bolt off trying to remove it, it means it’s well and truly stuck so when you get to extracting it, you’re dealing with the breakage but also the initial seizing. Whereas in your case it shouldn’t be that tightly held (I’m going to rashly assume it’s not overtightened, bottomed out, or crossthreaded 😉 )
Screw extractors are basically evil, especially in the smaller sizes where snapping off the tip and converting your broken bolt into a broken bolt with an incredibly hard screw extractor stuck into it is probably just as likely an outcome as success, unless you’re pretty good. Even in skilled hands it can go wrong. It’s also depressingly easy to screw up the drilling since helpfully the bolt is hard and the fork is soft. So all in all, best to go to someone who’s properly good at it, if you can.
If you want to do it yourself- centrepunch bolt. Soak it as well as you can with penetrating oil or diesel. Drill with left handed drill bit (no, that’s not a joke). Drilling might remove it by itself, and will also chuck a bit of heat into the bolt to help release it. Then screw extractor, biggest size you can use, and very very carefully.
Not being funny, but personally I’d just cable tie it- after all that’s how all my forks do it.