If you don't have time to get medical assistance then chances are you won't need it.

Do nothing to the cord, the baby will not bleed. The cord will go white and then the placenta will come away - leave it attached until the ambo arrives as it will make it easier for them to catergorically say it was your baby and you gave birth to it (the only problem i can foresee with papaerwork is that there's no "professional" to say they witnessed, not sure if DH would do, but with the placenta still attached there's no WAY the ambo's can think you stole tha babe and are passing it off as yours.

If baby is breathing and eating and your bleeding is not excessive and you have no tears needing stitches then you can absolutely stay at home - just tell the ambo's you'd rather stay put and arrange to have your GP call in ASAP (the next day if it's the middle of the night) to do all the normal Ped checks and make sure you're ok. They will probably stay with you an hour or two, to make sure your bleeding isn't going to increase (the first 2 hours after birth is the highest risk bit for PPH) and *might* pressure you to go in so they don't have to wait about, but you don't HAVE to go in.

I don't know about paperwork, it'd probably depend on situation and state, but these things MUST happen sometimes, so there will be a way, don't worry

If i were you i'd be planning a homebirth to save myself the worry!

Bx