Mistwell
Crusty Old Meatwad
Even if you (or your DM) rule that it only takes one hand, sheathing a weapon uses your free action, and drawing something from your pack uses your free action. So if your rogue dual wields the only option is to drop one of the weapons. Now, whether or not you and your DM decide that you can use a Healer's Kit not only with one hand but your offhand, is up to you.
Yes if you dual wield you will have a problem. I was not assuming dual wielding. You will need one free hand I assume. As for "offhand", I don't really think that's a thing in 5e for tool/object use.