A fuse isn't really needed, as if the detector draws more amps then it should then you've got bigger issues due to component failure. But if you are going to use a fuse, not sure but 300ma sounds a bit too higher to prevent further damage. Most machines I ever measured the amp draw on were very low. The Sovereign GT, for instance, draws about 50ma when not sounding off to a target and about 70ma when it is under load (sounding off to something). Being that your machine is an analog detector, it might very well be it's amp draw is much higher, and then a 300ma fuse would be a good idea depending on what it was. Best way to pick a fuse though would be to measure the amp draw of the detector at full volume, highest sensitivity possible, and while sounding off to a target. Then pick a fuse that is only perhaps 1/4th higher in amp raiting than the amp draw of the machine under highest load conditions. For instance, if the detector draws 100ma max, then I'd should for about a 125ma fuse. Perhaps a little higher (maybe 150ma) to insure against amp spikes at power up which can happen while the components energize.
Either way and regardless, great job on the mod. Detectors seem about 15 to 20 years behind in terms of battery technology. Simply no excuse to still being using nimhs in the factory rechargeable packs, or at least at the prices they often go for as nimhs are very cheap these days, and also at often the low capacity they have when there are nimhs with 2 or 3 times the capacity at very cheap prices, not to mention they often pair the pack with a simple wall transformer that doesn't terminate the charge when done or tell you that or are charging at such a snail's pace that it takes half a day to charge the pack.
I've gone lipo in my GT. Cheap, fast charging, and very light/compact. Lipos are very safe these days thanks to balance chargers.