Thats a shame, you might want to buy a small project box or something to put it in then, stop anymore shorts. Ideally track a new relay down.
If theres no letters before it, then im sure enough to say it will be quickblow. Time delay don't blow instantainiously, they allow for small surges for example when turning on equipment that has high in-rush currents. The worst that could ever happen is the fuse would blow again, but an ECU wouldn't have a high turn on current. Things like bulbs do.
How much gap? A 1.25 inch fuse is considerably bigger. (sorry just realised i said it was a 1/4 inch fuse above not 1 & 1/4
)