Hi.
I’m an old regular at this. My mom had a feeding tube and I have mastered the art of stashing medical supplies in LV!
Depending in the dimensions of your item, I recommend the toiletry 19. I would put the existing case right inside. It stands upright and has a wipeable interior. It’s great to hide your kit and even some crackers, etc. that you may need. It is easy and discreet.
I used the Toiletry 26 in my Neverfull for my mom. I had to carry syringes, water and osmolite (like a can of ensure or boost).