Most of the reported sides from hydrocortisone are from concentrations way over 1%, or other more potent topical steroids.
IMO as long as you only use it once per day max, you could probably use it forever. Since your face only absorbs 7% of HC, and the skin on your scalp is thicker so the absorbtion rate is even lower.
There have been people that have used 1% HC for years and years on their faces with no problems at all. Though, prolonged use will probably develope dependancy on it...So if you ever decided to not use it, you'd have withdrawl symptoms that lasted for a week or so.
Most peoples withdrawl symptoms would include very dry skin, burning/itching etc, possibly temporary skin discoloration. One user reported his skin turned an orange color and hurt extremely bad. But this user had used 1% HC for years on his face. Again, since we're talking about scalp usage, sides may not be as bad.
If you want to use topically, you can use 2x - 4x per day for a week, then drop down to 1x/day max. Maybe even EOD usage just to be extra safe. If you notice any local sides, discontinue, or drop usage in 1/2 and re-evaluate.
Cortaide has a 1% HC spray bottle which is super easy to apply. A few sprays on your scalp 1x/day and no nasty cream residue to deal with.