Any particular reason it has to be in the fridge?
The thing is, it is actually not recommended to store tropical fruit in the fridge. So mangos, bananas, kiwis... The other thing is that most fruit doesn't need to be refrigerated and will still stay fresh at room temperature (assuming room temp is between 20-25°C).
You can buy a bunch of green-yellow bananas and they will ripen throughout the week without going bad and leave them outside. Apples will last a long time outside of the fridge too - even in warmer/moister climates. So do citric fruit. Berries and grapes are probably the only thing I would refrigerate, as well as cut fruit. (Tbh I wouldn't refrigerate berries either because that makes them lose their taste, so I'd just eat them right away. They are a fleeting breeze of summer that should be enjoyed within the blink of an eye.)
Why do you need to limit yourself to one type of fruit? Idk your fruit portions, we eat so much fruit at home that I am shocked we haven't died of fructose induced liver cirrhosis yet. So get some greener bananas (store outside) for Tuesday and Wednesday, grapes in the fridge for Thursday and Friday, and bring something fresh like a mango for Monday? And just have a sack of apples as an emergency. They, like, really don't go bad. If you buy fruit that is not fully ripe yet, then as well, leave it outside, next to the apples ideally, and they will ripen by the middle/end of the week.
Also, veggies?
That's ham bro