You mentioned a wall charger 5V - 1000mA.
i.e. 1 Amp potentially. Posssibly more briefly with capacitance.
" Why the fuse?"
A circuit mistake by you or a careless moment could result in 1 Amp or more entering the circuit.
This could easily zap components.
A fuse (or some breaker) could provide some protection.
A little circuit might be saved with a 100mA fuse, for example.
"Do I must cut the male connector ?
Do you know any practical way to avoid this?"
- Well, obviously if you can find the corresponding female connector it would save you chopping it off.
Assuming you connect things correctly, it could also ensure the correct polarity of + and -.