You can getaway with the old olive but it's so cheap you can pick them up from good LBS.
I did mine after shortening hoses and cut at the lever side.
Shimano brakes are designed to get rid of the air via the lever. I didn't have to reblead either. If you do it at the caliper end, make sure the caliper bleed screw is open before you press the lever as it will move air bubbles around from the pressure. If the air is only in the caliper, then sure it's easy to get rid of by releasing the caliper bleed nipple.
If you cut the shimano brake at the lever, the closed end of the caliper will prevent loss of fluid and air getting in as the insert is tapped in gently and is hollow to prevent air being forced in.
It will drip from your lever if you press it so don't!
Cut at the lever hose, shoten, use new insert and olive for £1.60, reconnect, then undo the brake lever cover and top up then gently press lever and watch the odd bubble clear and the lever should still be tight.
Job done.
I'm glad I used new parts but you can do it with the old bits but funnynick has a point-takes a minute to stick the insert in and a new olive instead of making it fit for sake of flaffing around for ten minutes and besides your brakes could leak-it's your life.
If you're not sure then ask your decet LBS who will give you advice.
Cut the frame? geez just use some cable guide inserts that could screw into them.
But then again most onone's are cheap and the owners are not worried blng as it's there to be used and abused/replaced…ok I'm hiding under a stone now…
Just don't bish/bash/bob your brakes together at least-not stopping could kill you.
I forgive you for buying a onone… 😈
IGMC