There are 2 alternatives, you can get proper paint tape, 3M Fineline Tape Product code 6520. It's 3mm thick though so perhaps a bit too thick. It's a sort of greeny grey colour. They do a blue one too which is more flexible but if you leave it too long it comes off on it's own and it leaves a residue behind which is no good.
Alternative to that is
jammydog.com who do many many widths of tape, perfectly good enough for this, cheap, because it's thin you can sort of draw with it and get nice tight curves.
Or you could buy some liquid mask and a scalpel which I must say I'm sort of favouring at the moment, no blow throughs or miss masks, all in one go, nice and easy.