I had a mohawk for a fairly long time, and shaving didn't take too long - albeit, I didn't shave daily, although I did have to take some care to not shave off the middle bits. Why does shaving take so long? I assume it wouldn't take much longer than shaving your face. Slap some goo on your head in the shower, run a safety razor or a bic over all the bits, run your hand over it to feel for stubble, rinse, repeat, no?
I shaved my head for a solid year, and I had to be incredibly delicate because any nick or scratch and I would bleed like a stuck pig.
Sounds like cheap razors to me. Get a high quality razor + shaving gel and you'll never cut yourself. I've been shaving my head for 15 years and only bled once, from a crappy budget singly blade razor.
Shaving is something where you really REALLY have to test different things to figure out what works for you. For example some men really prefer Feather blades because they can get a really close shave with them. For me, those blades actually tear up my face to the point that I break out in a rash. Using the same technique and a Gillette Platinum blade I can get an incredibly close shave in two passes.