Tanning your scalp
I wouldn’t worry so much about tanning. The first few days, your scalp may be a bit red, that’s true. But again, it’s only for few days. I have heard some guys asking about the best season to shave their heads; I don’t think there is a “right season” for head shaving. In summertime, tanning occurs more quickly than in the winter (this isn’t so true in wintry cities when the reflection of the sun off snow and ice can intensify skin damage at least as great a rate as occurs in summer), but the tint difference between scalp and face will be greater. On the other hand, in the winter that difference is smaller, but it will take a longer time to tan your scalp.
Anyway, from my experience, after less than a week of normal everyday exposure, your scalp should get the right tan.

 

Male Pattern Baldness

Attention! Don’t try too hard and force your scalp to get the “right” tan in a short period by exposing it to the sun for long periods of time; you will burn it and put yourself at risk.

If you are still worried about the tanning thing (I understand that, but I’m telling you - it’s nothing), you will probably find self-tanning products helpful. I recommend self-tanning towels, I’ve never tried them, but they are extremely cheap and sound not bad at all.