One main issue that comes up often with regards to Hajj is about what is permissible to do and use for cleanliness.
It is definitely permissible to use cloths or towels, whether dry or dripped in water, to wipe or wash one’s face.
While the basic ruling is that it is prohibited to use perfumes during the state of Ihraam, it is understood that there are other products that are used that – while not intended to be scented – contain certain perfumes or fragrances within them. This includes soap, toothpaste, and the like.
It is urged that the Muhrim strongly avoid using scented soaps and lotions, and toothpaste insofar as one is able to avoid a scented one, but it is not completely prohibited (especially with regards to something like toothpaste.
With regards to chewing gum, some scholars are of the opinion that it is preferred to avoid it if it contains a strong fragrance, but others consider it to be permissible as it is a type of edible product.
As for washing one’s clothes with detergent and using moisturisers, yes, it is permissible to do both, with emphasis on avoiding perfumed or strongly scented products as much as possible.
And Allah knows best.