USB plug adaptation for Dremel 7750
Looking at the specifications of that Dremel it seems to have a battery voltage of 4.8V using NiMH technology. Which sounds like 4 cells in series to me at a nominal 1.2V.
Now nominal voltage is not charge voltage to fully charge it the battery voltage should reach closer to 1.6V per cell or 6.4V for the device. The included adapter was probably unregulated so the voltage rose significantly above the marked 5V depending on load which would work as a dumb charger for NiMH probably sacrificing some life due to poor charging characteristics.
Your nice regulated 5V from your USB compatible adapters is not going to charge that Dremel. You need something that behaves more like the original adapter.