@Hsnopi
Things to consider... The AWG of a solid core wire will have a smaller diameter than stranded wires.
Stranded wire varies slightly in diameter... but when I say slightly, I mean you will most likely not run into a condition where this is important.
Please also note that the Cat.5 cable you used is also available in stranded.
Solid core is used in places where the wires are fixed and will not move, stranded are used for mobile connections. IE, handsets and headsets. Stranded Cat.5 for example is sold to consumers more often than not for their desktops and laptops where solid core is bought by contractors and electricians for wiring homes with.
Additionally, if you have schematics, you may be able to swap out the wire for an electrically equal or better version if you know what to expect when it comes to the amperage. There is no harm putting in more capable wiring. If you are wanting to make some 'upgrades', you could swap out many of the parts with easily accessible and replaceable parts so if something breaks later on, you can go buy a new cord from a local best-buy or something and simply plug it in.
If you are wanting to stay closer to 'stock' this will require attention to detail, and I wish you luck. If you have more questions just ask.