Yes they can because their hands become tahir (externally tahir) just after completion of third ghusl of mayyit. So giving the kafan to the same dead body has no problem.

Ruling 211. The plank or stone on which a corpse is given ghusl, and the cloth with which the private parts of a corpse are covered, and the hands of the person who gives ghusl – all of these things that are washed with the corpse become pure once the ghusl is complete.

https://www.sistani.org/english/book/48/2146/

In fact there are two types of najasah, one is external and the other is internal which is called in Islamic Term (Najasat-e-Zahiri and Najasat-e-batini) so when a person touches a dead body with his hands after being cold, his hands become externally najis as dead body is one of the najasaat but a ghusl also becomes obligatory on him due to internal najasah which is called "ghusl e mass e mayyit" just like that if ghusl e janabat is wajib upon someone he is internally impure so he can't offer namaz etc. But his hands and body are tahir except in the case that his body or hands became najis by another najasah like blood etc.
Therefore if the same team is doing kafan who have done ghusl e mayyit, before taking ghusle masse mayyit, I don't see any problem in that according to Islamic rulings. If we say that it's better to have two teams one for ghusl and other for kafan, this recommendation should also be proved by Islamic laws and authorities.