Spindles can be bought separately.

Most bottom brackets sold today are one-piece cartridge types; can I gather from the question that you want just the spindle and will use the cups and cones somehow to mount it?

I think the shortest spindle I have ever run across is about 105mm. Maybe something that was track specific could have been a couple of mm's less than that.

Depending on how reliable you needed this thing to be, you could maybe grind down the end of a spindle to save a few more mm's.

Please, please show us pictures or plans or something so that we can see this beast you are building!!!

jim