Help needed to wire a dremel setup

I have an old battery operated dremel that I have cut down to just the motor casing,the low/hi speed switch and everything else has been cut away. I have 2 lithium ion (4.4volt each) that I would like to run the dremel with. My issue is I would like to set it up so that I can run the dremel at 2 different speeds using the batteries in parallel (4.4volt) for the slow speed and in series (8.8volt) to run at hi speed. First I do not know what kind of switch I would need to use that can switch between the two wirings and I do not know how I would wire the switch to the batteries to accomplise this. Any help would be greatly appreciated.

Using a DPDT switch (or relay, if you like), the schematic below will work:

View attachment 60864

The current switch position is for series operation.

You'll still need the ON/OFF switch that I assume is already part of the Dremel setup.

(And yes, I know, that's a relay image - couldn't find the DPDT switch compenent...).