Well, this one looks as long as the original horn, so I think it could tolerate being slightly shorter (the original horn just looked too long and unbalanced to my eyes). I think 4cm would be plenty.
If you get really stuck and want to find out where this one came from, I got it in a custom collar from Oh! Bondage. she is a lovely UK-based lady and I'm sure she wouldn't mind telling you where she gets her studs from. Alternatively, D is about to get a collar made by her and I could ask her if she would pop in a spare long stud. I will go and find the website.
ETA: Website here
http://www.ohbondage.co.uk/black-pvc-silver-leather-spiked-collar-mix-coned-spikes.htmlSo, they are 2" cone spikes. I now remember that I swapped over the smaller studs (1") with longer ones (1 1/2") that I got in a collar of the £1 table from that shop in the Lanes. They only have a few of each collar, but it is definitely worth a poke around.