Protection circuit with polyfuse and zener
The polyfuses (and fuses in general) take quite some time to trip and precision Zener might not survive long enough.
Did you consider specified TVS (Transient Voltage Suppressor) or ESD (electrostatic discharge) Diodes instead of the &quot;Zener&quot; ? Those are also Zener diodes, but not so much optimized for low noise or precision. Instead they can handle very large surge currents.
The fuse rating should have a current closer to 200mA, so it will trip faster. Getting one specced for e.g. 300-400 mA is sufficient, depending on how long you need that peak current. It can be good to spec the fuse lower than your peak current to accelerate fault tripping. But this is not an option, if you need the peak current for several seconds or more. Consult the fuse datasheet for trip speed at various current levels. The voltage rating of the fuse should be much higher than 6 V, compatible with the largest voltage that you want to protect against.
Littlefuse offers this plot in their PPTC datasheet of the part you chose:

So you see, that even picking something like the 0.35A / 30V part might be to slow to trip. You can try a few different parts though, to see what works.
As for the Diode, something beefy in e.g. a DO214 package has enough current capability. In the datasheet of STMicro for the SMBJ5.0A/CA there is this plot:

The important parameter is the minimum breakdown voltage, which needs to be high than your intended supply voltage. A &quot;5 Volt&quot; TVS usually has about 6-6.5V minimum breakdown so would be suitable.
For much higher current, there is the option for a resettable crowbar circuit if you have trouble finding a beefy enough diode. Such circuits are used for higher power settings usually and not needed here, I guess.