Here is a life hack that may be just what you need but, if not, will be useful for more other applications than you'd ever have imagined.
There is a low cost and very effective sanitiser available. I do not know if it will damage your screen coating, but I'd expect that it wouldn't.
The material, which I'll call Baq for short, is used in the majority of disinfectants and sanitisers. Also sold as carpet shampoo, floor wash, hand sanitiser, mouthwash, mould preventer, moss remover, pool sanitiser and more. Despite its apparently fearsome abilities it is also used at low concentrations, as an oral disinfectant. It is variously known as eg Quaternary ammonium salts / Lauryl dimethyl benzyl alkonium chloride, Benzyl alkonium chloride and more. Once you've seen it mentioned a few times you'll find it under a range of similar names in many (possibly most) cleaning and sanitising products.
Read the ingredient labels on as many disinfectants as you can find. Here most use Baq. The cost per active ingredient varies widely.
Baq is available at a range of concentrations and prices that usually utterly fail to reflect how cheap it really is. Here (in New Zealand) I can buy 2 litres (about half a gallon) of 2% concentrated baq for $2. That can be diluted 20 to 1 (20 parts of water to 1 part of Baq) to make (close enough to) 0.1% Baq solution. This cam be used as a hand sanitiser, kitchen bench wipe down, disc-cloth soaker, shower cleaner , general disinfectant - and cellphone screen cleaner. I would be surprised if it caused screen damage but, as they say, try it in an unimportant area first.
How good is it? - At about 0.1% to 0.25% concentration it is sold here in Chemist shops as an approved hand sanitiser which is superior overall to 65%+ alcohol hand sanitiser. This costs over $10 for 250 ml x say 0.25%, so is about
$10/$2 x 2l/250ml x 2%/0.25% = 10 x 8 x 8 = 600+ times dearer per active ingredient that the disinfectant I buy in the local supermarket. And no more effective.
As a general purpose value or money life-hack it's about as good as they come.
For smart phone sanitising it may be as well.