Which wire for internal recabling my speakers?

Neotech solid core is your best choice. It is not analytical sounding. In fact, it has nice body and warmth. I use it and prefer it over my long time favorite Duelund.

Use 18 - 20 gauge on the tweeter.  12 gauge on the woofer.  16 gauge is fine on the mids.  Great internal wire for speakers.  Again, not bright or analytical after break in.  It has good warmth. 

I wouldn’t arbitrarily change speaker wires brand and model from what is in there already. The sole exception would be possibly moving up to a higher model in the same brand ( if possible ), , with the view to maintaining the same bespoke cables sonic signature. 

Agree with grannyring on the Neotech. I use it and will add that it is finely detailed too without being cold or chromium etched.

but.... I suspect it to be too analytical and on the dry side, without richness in harmonics.

Thank you, so neotech is a good choice even for natural timbre.

My crossover has this cuts.

Tweeter works above 2000hz, mid between 2000 and 200 Hz and  woofers below 200hz.

Could be ok with 18awg for tweeters, 14 for midrange (because also works at 200hz) and 12awg for woofers?

Fine.   

I suggest that you check out the Audience Auric 18 and 21 awg wire.  IT is exactly what you are looking for in terms of quality of copper and quality of sound.  Happy Listening!

I like the Mundorf Angelique.  I've used it in speakers and amps.

Why not the same speaker cable you’re already using from amps to speakers?

The Neotech 12 gauge solid core is fairly stiff and unwieldy. I'd stay at 14 or higher.

Could be ok with 18awg for tweeters, 14 for midrange (because also works at 200hz) and 12awg for woofers?

OCC single crystal wire is never dry and without richness but you shouldn't be using solid core for internal wiring you should use multi-stranded but OCC single crystal is definitely the best wire to use, 14 to 16 gauge. I use neotech OCC in my speakers when I rewired them and I got a 10 to 15% improvement right across the board.

The wire used in my loudspeakers is unbranded so I don't know where to buy, besides is not long enough to put crossover outside loudspeakers.

Interesting question

I bought a faulty pair of Proacs and looking inside the cables was pretty ordinary looking.

I asked my repair man about upgrading and he told me that the present cable was decent and any upgrade might not produce worthwhile results

So I kept the old cable in but still have no idea whether I missed an opportunity

Exactly which model numbers of Neotech are you talking about and what website sells it?

whatever you decide, Would we use a twisted pair or a single strand? Would we get a lower inductance with a twisted pair? Would it make any difference? It may be a lot harder to solder two terminations versus one!

Solid core copper sounds best compared to stranded in my experience. The Neotech line of UPOCC is sold at Sonic Craft. Jeff the owner of Sonic Craft is expert on speaker crossovers and internal wiring and also praises the Neotech line of solid core bulk cable. Here is a link.

https://www.soniccraft.com/index.php/neotech-wire-teflon-solid-cu-c-296_175_183_221?osCsid=9e253907f8dd2263322a229177a6ba13

You should twist the positive and negative runs from the binding posts and drivers to the crossover board to help reduce noise.  This is especially true if the runs are longer as in tower speakers. 
 

Stranded Neotech wire is a tad easier to work with being less stiff, but it is not as focused and pure sounding. I like using solid core wire internally as it easily bends in place and stays put! This is important. If you have some skills and experience using 12 gauge on the woofer is ideal. If really not that experienced, then 14 gauge is a bit easier to solder and work with.  
 

You can email Jeff at Sonic Craft with your project questions as he is very knowledgeable and will help. 

DH Labs "Silversonic"

I would expect stranded wire to have some kind of instabilities owing to the vibrations inside a cabinet.  My vote is for solid wire, if you're concerned about this at all.

 Remove the crossover and hang it from rubber bands? Seriously?

Thanks, almost missed that.

Grunter, look through the pics, rubber bands are a good cheap isolation solution. They do however not last very long. Over time they stretch and break. You have the right idea, just be a lot better with springs. Nobsound are cheap and highly effective. Townshend Pods are a lot better. Second to last picture shows mine on a bench, same thing is inside my Moabs and works great.  

https://systems.audiogon.com/systems/8367

If you elect to go Nobsound I suggest hot glue individual springs under your crossover board. Experiment first on a bench to find how many and where, then hot glue in place. Will only need at most 4 per board. This will leave you with the Nobsound footers and enough springs to do another component or two.