I am assuming that the Three are like the One in the sense that they
must physically be worn in order to utilise their power.
Evidently so. From The Silmarillion, Of the Rings of Power and the Third Age:
As soon as Sauron set the One Ring upon his finger [the Elves] were aware of
him; and they knew him, and perceived that he would be master of them,
and of all that they wrought. Then in anger and fear they took off
So yes, it appears wearing the Rings was necessary in order to use them, and to be dominated by Sauron via them. We can conclude that during the time of LotR, Galadriel, Elrond, and Gandalf were wearing theirs, just not "openly."
Also, immediately following in the same paragraph:
But [Sauron], finding that he was betrayed and that the Elves were not
deceived, was filled with wrath; and he came against them with open
war, demanding that all the rings should be delivered to him, since
the Elven-smiths could not have attained to their making without his
lore and counsel. But the Elves fled from him; and three of their
rings they saved, and bore them away, and hid them.
And a little lower down:
But Sauron gathered into his hands all the remaining Rings of Power;
and he dealt them out to the other peoples of Middle-earth, hoping
thus to bring under his sway all those that desired secret power
beyond the measure of their kind. Seven rings he gave to the Dwarves;
but to Men he gave nine, for Men proved in this matter as in others
the readiest to his will.
From these passages we can see all the rings means all nineteen, which is the sum of nine, seven, and three. The Elves took all of them off. The seven for the Dwarves, and the nine for Men, were originally made by Elves for Elves. The whole situation was a set-up for Sauron to control the Elves, but it didn't work. He hadn't taken into account the fact rings can be removed. Giving rings to the others was an improvised plan B.
The failed project to control the Elves was the reason Sauron put so much of his power into the One Ring to begin with. I won't spoil the outcome for those just now coming across this story.