I've blown a couple fuses a simple short probably won't blow it, you just lose power. If you have a good short or something significant you'll blow the fuse. To completely melt the fuse holder you've got something else going on. Either there is a bad wire in the fuse holder (I've had this) or something is connected to something very wrong. The fuse holder is probably 40 years old with brittle wires and bad connections.
I agree with evanphi, you've got this - wiring feels overwhelming but gets under control really quickly. I wouldn't pull the handle bar wires yet either, they're a pain and pulling them in and out causes more damage.
First - Get a simple current tester, they're about $6 from any auto or home depot, have a clip that you attach to something metal and a long pokey attached to a light. You can poke through insulation if needed to check a current and easily get up into a connector. Light goes on, you're live. This is important, I used it probably 50 times during the last wire-up.
Next - Get a new fuse holder w/fuse, another $5 from any auto store.
Then - Unplug everything in the headlamp and walk through each circuit one at a time. I really recommend the horn first, it's isolated to one control and the horn, it's super easy to see the wires all the way through. If you can't get current to the horn trace it back to the ignition switch, make sure power is going in and coming out. If that works now you know you're good from the battery through the ignition switch to the headlamp and you can move onto the blinkers - same control plus the indicator light. If that works you can move over to the other control with the lights then the start button and start/stop switch.
It would be really nice to pick up some terminal connectors so you can hook up the new fuse properly and replace any bad connectors with new ones, but you can get by with just electrical tape.
All in you'll have spent $10 and two hours vs. $200 at the shop and who knows how long to get your bike back.