Does transubstantiation require that the priest physically touch the host
The priest will have one host in hands during the words of consecration but there may be others that are also consecrated which he will not physically touch.
He holds the chalice when he says the words of consecration over the wine but he does not physically touch the wine.
For the Eucharist to be confected he must be a validly ordained priest. We should generally assume that the priest on the altar is.
He must use valid matter and again without contrary evidence we should have trust that our priests are using the proper matter.
The priest must use the correct form, which is the words he says, and he should according to the old saying, do the red and
say the black, i.e. he should use the exact words found in the Missal.
It is also important that the priest has the correct intent and I think this is what your question is really about. The priest has to intend that bread and wine are to be consecrated. Normally, this would be what is on the altar but if it were some major event with huge numbers of communicants ciboria with hosts could be on a table. The elements are consecrated that the priests intends should be consecrated.
Whilst, of course, only a priest can do this and in doing so he acts
in persona Christi, it is the Holy Spirit that brings about transubstantiation and not the priest.