If you do end up replacing the axle with another, there used to be a tool available, maybe still is somewhere, that would thread onto the end of your replacement axle, and would help with pushing the old axle out thru all of the wheels, collars, spacers until the new axle was in.
The tool is a length of round rod that was the same diameter as the axle, and coned/rounded on the leading end to help pick up each component as it made it's way thru, pushing out the old axle. The tool would then be removed from the new axle and you're good to add the nut and tighten/adjust the track.
Without this tool, you could try to duplicate it by winding some tough tape (electrical comes to mind) in a cone shape on the threads of the new axle, just don't make the tape larger than than the axle diameter. You might have to tear the tape into narrow sections to build up the large part of the cone, and you could try to overlap the tape over the very end of the axle/threads to help with lead-in as the axle slides thru and meets each component. Some grease on the tape and axle may help, as well as turning the axle (in the direction that won't unwind the tape) as it goes in.
Either of these would obviously reverse the axle direction in the sled, so if you wanted more practice at this you could pick up yet another axle and push it back thru the other way so your direction is back to normal!

, but I don't think I'd worry about it too much...