Question on speaker hookup wire upgrade

How about individually wrapped and kept apart. That should leave you covered.
I am not sure by your "wiring inside the woofer" apart from the last leads to the to the terminals. It is hard to envision rewiring the internals of the woofer like its voice coil etc.

It may be better to leave them separated - IF you can maintain a separation distance of at least, say, 6-8" along their length. If not, then it may be better to twist them together. If you're still in any doubt, you can always try it one way awhile and then compare to the other. But, usually the full-range difference results in some change in openness in the upper mids or highs, although I would expect that difference to usually be slight, if at all. But, since you're dealing with woofers here, I would say there may not be normally much of anything amiss soundwise either way, really. Hope this helps.

Thank you both for your answers!

Wrap them as tight as you can (twisted pair). It will increase capacitance
and resistance (both not important) and reduce inductance (also not
important with the woofer). What might be important is reduction of
ambient electrical noise that wires can pick-up and feed back into amplifier.
Twisted pair effectively reduces noise pick-up for frequencies that have
much longer wavelength than twist pitch.