connecting the fibre modem to router

[#1]

Is there any significance to the colour of the supplied network cables supplied. The red one is used to go between the two boxes and yellow from the router to PC.
The reason i ask, is the cable supplied is too long. I'd prefer to use a shorted Cat 6 cable, but unsure if it matters or is a "must use this" cable.

Cheers

[#2]

When I connected mine up from what I could see they are bog standard cat5e patch cables.  The colours are probably simply there to match the red port on the router and the others being yellow.  Maybe it also helps if support start asking you to unplug cables but functionally there is not a bit of difference I could see.
Other than you have a short length of cat6 I wouldn't bother getting one specially for it as there will be zero performance difference between any fully functional ethernet cable of any standard over the distance we are discussing here.  Also don't make it shorter in the expectation of it helping or improving something unless the difference is tens or hundreds of metres and even then the differences will be measured in nano-somethings.  Only reason I can think of for wanting it shorter is your OCD is cutting in like mine did and you want it neater 

[#3]

ANY cat5e or cat6 cable should work just fine, a 'straight through' or 'patch' cable is probably best but most equipment nowadays will also accept a 'crossover' type.  For short distances a cat5 is usually perfectly adequate (particularly between the modem and router which should never need more than 100MB/s).