Believe it or not, but using all red wires is how it should be done. The reason it isn't is because double red is not as easy to obtain, so most would use standard red and black, and the black should have a red marking on it to indicate it is live.
Changing the switch is actually easier than you think. The switch you have is known as a 3 gang 2 way switch. The switch you need to buy MUST BE 3 gang 2 way (Yes the same configuration)
You buy an indelible pen (black) (Or a self-adhesive label maker)
You mark each wire with a number OR number of rings Each number is one more than the previous number In the case of the "link wires" treat it as two separate wires so each end gets a different number.
Then take a few more pictures showing where each numbered wire is. (You take several pictures so you can see all the wires) Then you look at the switch it will have markings such as C, L1 & L2 or it may be L1, L2 & L3 Make sure you take another picture with your now marked wires showing the marks on the switch with the wires still in place.
Make sure ALL the pictures are in FOCUS (if not delete and take again)
Your new switch will also have markings
Turn the electricity off and swap the two switches over.
Your new switch could have either configuration of numbers, it will not have both.
For your reference
C = L1 L1 = L2 L2 = L3
You may be lucky and the new switch will have the same markings as the existing switch.
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