Daf Yomi - Yoma 70 - Removal of the Ladle

Two Acharonim (Mikdash Dovid and Toras Hakodesh) have a similar chakirah regarding the removal of the כף from the Kodesh Hakodoshim. Which hand does the kohen gadol use to remove the ladle? He entered with it in his left hand, but here it is a shaila. The reason he holds it in his left hand when entering is because the machta (firepan) was heavy and he was compeled to carry that with his right hand. Do we say that in the removal of these keilim, he should use his right hand for the כף, which is more important or do we say that he should use his left hand, for once the carrying of the ladle was done with his right hand, it should always remain that way?

I was wondering as to why they are assuming that it had to be done with two hands. Could he not remove both of them with his right hand? They were not heavy or hot at this time?