Basculer can be used with vers but not à so we say:

Basculer vers le clavier qwerty

and not

Basculer au clavier qwerty

On the other hand, both de x à y and de x vers y are possible.

In the first sentence, the move is completed (or is described as a whole) while in the second one, the move is ongoing. That doesn’t make a significant difference when applying to keyboard settings so both forms are possible and acceptable.

We can also say:

Je bascule d‘azerty en qwerty.

I would use:

Je n’utilise pas qu’un seul type de clavier, azerty ou qwerty. Je passe de l’un à l’autre quand ça¹ me chante.

¹_{Quand bon me chante sounds odd. It’s usually either quand bon me semble or quand ça me chante}