Converting a Dremel 10.8 V rotary tool to use Bosch 10.8/12 V batteries - 2 attachments

I just converted a Dremel 10.8 V rotary tool to use Bosch 10.8 V batteries. I always have the rotary tool immediately in front of me, so the battery will either be worn on a neck strap or be set down near the work. The wires coming from the rotary tool plug into the battery, using a socket taken from another Bosch tool.

Should I expect a problem using a Bosch 12 V MAX battery in the 10.8 V Dremel rotary tool? The speed dial on the rotary tool plainly says "10.8 V". Included are two small pics of chips in the rotary tool.

Thanks.

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