Limited mobility riders ... how do you carry your kit

TLDR: how do you carry your stick when on the spare bike?

I realise this is somewhat niche, but welcome responses from all.

I'm limited mobility... I can walk short distances, but require a stick to do so safely.

My normal commuter has a pannier rack, and the laptop / change of clothes go in a pannier.

I was strapping my wooden stick to the crossbar; this had the downside of becoming uncomfortable on the inside of my thigh due to the additional width.

I then got a two segment aluminium stick, and was collapsing it and strapping it to the top of the pannier rack, with the handle to the rear and sticking out less than 100mm from the end of the rack.

My commuter is currently out of action with an unknown knocking coming from the motor (Bosch ActiveLine Plus), and my other bike does not have a pannier rack. Other bike is brand new, less than 150 miles done.

I have an active travel commute:
AM: 3 miles to station, train ride then 8 miles station to office.
PM option 1: 40 miles office to home
PM option 2: 8 miles office to station, train then 8 miles station to home
PM option 3: 6 miles office to station, train then 3 miles station to home.

Option B: drive 3 miles to station, train, walk 1/4mile to the office and reverse in the afternoon.

I don't want to do Option B as I'm missing the riding - both physically and mentally.

I'm discounting PM option 1 as I don't fancy 40 miles with a laptop on my back ...

So, option 2 and 3 are viable ... and here's the question:

How would you carry your stick?

Would you strap the full length wooden one to the cross-bar and put up with the inconvenience and risk to the paint
Or
Somehow strap the shortend aluminium one to the backpack in a vertical arrangement. (Don't think I'd get away with strapping it horizontally 🤣🤣)