Ok, we have the by the book, what Mearls has said, and how you probably want to play this in your game.

By the book, draw or stow can be done for free, you can do one of these per turn as the part of a move or action. However, if you want to do both, you’re stuck burning your action to do so. If you’re TWF you’re in an even worse way, (though the Dual Wielder feat fixes the action economy here).

PHB page p190 states:

You can also interact with one object or feature of the environment for free, during either your move or your action.

Draw or sheathe a sword

Mearls has said in tweets that you’re OK to use your free action to swap weapons rather than spend your action to draw and stow. That the intent here was to curb over use and also to not burn you on the action economy to swap weapons. (see this convo)

Ultimately, for your game, I think it’s up to you to decide between these two rulings. Personally, I prefer my character to not get burned by the action economy here and have ruled that quick swaps of weapons (especially when it’s commonly used load outs) can be done as part of the attack. I don’t make a stink about it, and assume the PCs in my games are competent at what they do.

If you really have to make this work, dropping your weapon is completely action-less, so you could do that. It’s messy, and prone to issues if you get moved off your space (you can’t pick your weapon back up), but maybe that’s just the cost of weapon juggling?