Worth the effort? Cabling inside sub

@douglas_schroeder   has it correct. 

If you want an easy and inexpensive, but good upgrade to the leads between the amp and the subwoofer, go to Lowes or Home Depot and pick up a couple of spools of Southwire 10 gauge THHN stranded copper wire, red and black.  On each run, wind the cables around each other (twisted pair) at maybe one to two complete turns per foot.  

The 12 gauge stranded version of this stranded wire wound two to four turns per foot is really quite good for amp-to-main speaker runs.  

Absolutely not, stick to the big electrolytics.

Now, on the other hand, you sound ready to build your own speaker kit, come over to the dark side and let me show you how you can start ....

Just a caution about the wires from the RCA’s - they look like PTFE (teflon).

When PTFE is heated to soldering temperatures, it begins to decompose, and the decomposition products include one of the most dangerous gasses known, HF. If those wires really are PTFE, best to avoid messing with them.

There are very few things as slippery as PTFE, but cross-linked polyester, which is also used in quality audio cables, is similar. If they are slippery like PTFE or cross-linked polyester, you probably shouldn’t chance it for safety reasons. And you can’t buy better wires anyway.

Suggest that if they are real slippery, don’t change them.

I always make a practice of using pure four nines fine silver wire for speaker internal hookup. It makes a notable difference in presence and sound stage

For short runs of line level signal, especially low frequency, the main thing you are hearing is insulation (the physical phenomenon is called dielectric absorption, or DA). PTFE and cross-linked polyester are the best conventional alternative (only air and vacuum are better).