Anyway is this not the sort of problem 3d printers* were made to solve? Indeed it appears someone else had the issue and solved it back in 2013 https://www.thingiverse.com/thing:50898
*I am not a huge fan of additive processes for this sort of thing so would probably come the other way and use a CNC mill to mill down a block of plastic.
Getting it to match the particular shade of pink (consider also that the thing has had several decades to age and change) might be a harder trick. If you are using a CNC rather than a 3d printer then you have a chance to find a block of plastic of a suitable colour right off the bat.
Plastic dyeing can be done by mere mortals with stuff like https://www.vinyldye.co.uk/All-Vinyl-Dye-Color-Sprays/Raspberry-Vinyl-Dye-Plastic-Paint-By-TRG , or taken to places which will do it but I am not sure what to point you at for this if you don't want it to cost a quite a bit.
Modern consumer level dyes and paints and small volume stuff is actually really good. It is not like basic spray paint or any model paints you might have seen which chip if you look at them harshly and rub off if an insect breathes on it.
I do agree 3d printing is not ideal for a cosmetic thing (though an acetone rub will get you a pretty nice surface finish), which is why I suggested CNC instead. It is a lot of plastic to remove if you are going to try to do it all in one piece (no making a long tag and heat bending it or something) but it is only plastic so it is not that bad. Find a local equivalent of something like https://www.tapplastics.com/ or maybe have a word with a plastic manufacturer around you (there are usually a few around) and see if you can raid their scrap bin.
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