How can I make a 3D tool change the .json model?

Create two models: the sword and the axe (or just make a practice texture for sword and axe). Create the first weapon, the sword. Then set a trigger >> on right click >> Set item in main hand of event/target entity to 1 {axe}, save it. Now do the same with the axe ... but pointing back to the sword (when right clicked). Save and test.

Have fun

how could I make the enchantments of the original weapon change to the new weapon with the different model

For that you must create a procedure that can find the specific enchantment from weapon #1 and then transfer it to weapon #2 (can be done, but will be very complex).  

can a 3D weapon change texture?

 It does not change texture, you create a procedure that tell it to change texture. Make that weapon (make more than one model with several textures), then when right click change weapon #1 to weapon #2 with an animated texture. Create the 3d weapon with animated texture in Blockbench.

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When you say "I want to make a sword that when right clicking changes its texture", it is simply creating the same 3d weapons twice with different textures in Blobkbench ... add them in MCreator, in the triggers >>> When right click, create a procedure that switches the weapon in main hand to the new animated weapon (with animated texture), then do the same to the animated weapon to switch back When right clicked to the non animated weapon.