I would only take off the straps if the pack flies as checked-in luggage and in that case I would put them in the pack.
If so, you will need to do it before handing it in as the luggage drop off. If there is a security check before the drop off, you may as well wait till that has been past, but if arriving at the airport by car and your pack having a good way to lift it without the backpack straps, you may want to keep them off while packing, so you know you have enough space to put them in.
Even when shrink wrapping the pack I would take off the straps and put them into the pack. Less danger of anything getting damaged.
The only reason to keep straps on the pack when it goes into hold luggage is when you undo the fit of the pack by taking off the straps and you have to adjust them all over again when you put them back on and the pack is adjusted well already. In that case I would (and have) left them on, closed on the outside of the pack as tight as possible and hoped for the best, wrapping not available where I flew. I would shrink wrap in that case.
When using such a backpack for carry on luggage I will not take off any straps unless I need to do so to make it fit the size box for carry-on luggage, in which case I will put them away as near as possible and put them back as soon as possible.