I shaved mine a couple years back after it started thinning near the front. People say it suits me and people that have never seen me with hair day they can't imagine and and I look better without etc.
I bought a Remington quick cut and I just do head and face with it so it is all the same length. I don't use an attachment and do it every 3 days.
The main thing for me and it might help you to, is how nice it is to not worry about it when it's windy or raining. I used to be constantly messing with my hair trying to make sure it didn't look 'thin' when I was out our any time I passed a reflection, now I simply don't have to worry
I'd say give it a go, worst case you just grow it back after it really doesn't take long when it is that short.