Rechargable neck fans - goes around your neck, charges with phone charger and totally hands free. They last up to 8 hours depending on the speed you have them.
Bruidine cream when you do get chapped skin/sweat rash/torn skin etc. Never known anything - not even sudacrem - mend it as fast.
Shower when you get back to the hotel room and change your clothes.
Leave your air conditioning as low as possible but leave a note saying that you wish it to remain this low - housekeeping always turned mine back up when I was in London last year - bloody annoying.
Liquid talc. Something for thigh chub rub. Also don't be afraid - rather graphic - to put some up onto the area near bumcheeks where full briefs go (obviously away from membranes etc) as I can feel it there sometimes but only tealise it when I go for a wee and the skin burns
Lots of water - bottles/drinks out and about/refillable bottles etc. Keep hydrated as you will sweat it out faster than you can put it in.
Electrolyte tablets - I use the High5 zero ones as I have hyperhidrosis (excessive sweating) and I lose a lot of the electrolytes I need and this gets them back faster. Literally one dissolved in a glass or bottle of water and I feel a lot better a lot quicker than just water/soft drinks etc. It also helps with cramps.
Handheld fan you can put on the bedside table somehow (ones I've seen in boyes have a circlular base you can fit into to use as a charging stand - I can't sleep without a fan in the summer.
A good antiperspirant deoderant that doesn't mark clothes.
There are some wipes etc called sweatblock that is meant to help sweating on the face when you put them on. You apply to your face the night before (avoiding eyes, nose and mouth) and go to sleep and then wash off in the morning. This iis meant to help with heavy facial sweating. I find they don't work but I do have full body hyperhidrosis and sweat from top of my head to toenails so even though they are for HH I'm probably too big a challenge for them haha. You must have a DRY face before putting them on or ouch.
There's also deoderants for HH called Odaban and perspirex (and others) that are to help with heavy sweating too. Again they area must be bone dry (and I mean bone dry - like dried with a hairdryer as well as a towel) or you will be very very sore but applied at night 7 days a week for a couple of weeks can reduce or remove sweating during the day. These ones I don't recomend for your face as you will be v sore and v frozen and if it drips in your eyes - ow!!!
Cooling towels. Special fabric you wet and wrap around your neck and wipe your face etc. If they warm up you simply 'snap them' (ie quick pulling from middle out two/three times in a row) and they cool off. You can also wear as a turban type/hairband too - www.amazon.co.uk/cooling-towels/s?k=cooling+towels You can also rewet them where possible too. Some come with their own little plastic pot or little bag to keep them in.
Chillow - if you can take it (I don't go abroad so don't know the rules) and keep it in a fridge during the day (mini bar?) and then lay your face in it .... heaven. Bit extra to add to the packing though haha!
Natural fibre clothing - especially underwear where possible.