I got these sticks, caps, and toolkit. Honestly, I prefer the normal joycon caps over the vita caps even though they're a little bit wide. If you do get the caps, just know that a set only has 1 of each, so get 2 sets if you want to use the same on both sides.
https://www.amazon.com/dp/B08BL4LY84?ref=ppx_pop_mob_ap_share https://www.amazon.com/dp/B06XKHJC5C?ref=ppx_pop_mob_ap_share https://www.amazon.com/dp/B07V3TDP49?ref=ppx_pop_mob_ap_share
Not OP but I just installed these and they work great. They are slightly bigger than the opening of the insert that is inside the shell. I just lightly wiggled the joystick and pressed until it came through the opening. Also the price is not bad and you get 4 of them.
Joycon Joystick Replacement 4... https://www.amazon.com/dp/B08BL4LY84?ref=ppx_pop_mob_ap_share
You can get a pack of joysticks for cheap (you should have them anyway for joystick drift later on down the road). It just takes the right screwdriver (make sure you don't skimp on this because a stripped screw is a PITA) and some patience to remove swap out joysticks. I've used these:
https://www.amazon.com/Joycon-Joystick-Replacement-Controller-Thumbstick/dp/B08BL4LY84/
to fix my drift issues 'cause I didn't want to wait to send them through Nintendo for free replacements.