Is it safe to change battery replacement for equivalent with similar voltage?
The 10s NiCd battery pack will return approximately 10V - 12V from &quot;flat&quot; to fully charged. It will still provide some energy below 10V but only a small percentage of total.
The 3.6V or 3.7V voltage of a LiIon cell is the nominal or mean voltage during operation - NOT the maximum voltage
A loaded LiIon cell has a voltage range of about 3V to 4V (4.2V absolute max unloaded) so a 4S battery will return 12V - 16V from flat to fully charged. This may be more that your drill will reasonably tolerate (and may not). A 3S battery will return about 9V-12V.
The maximum allowed loaded current of a LiIon cell depends on cell type. Some are optimised for maximum energy and usually have a low maximum allowed discharge current. Others are optimised for maximum power output with (usually) lower energy capacity.
In this application, using &quot;power&quot; rated high discharge rate cells is required. A power cell, depending on brand and model, may allow a 5C - 10C discharge rate, and perhaps higher again in very short bursts. For a cell with about 3 Ah capacity and 10C maximum allowed  discharge rate this corresponds to 15 - 30A. For a 3S pack this is a nominal power of
3.7V x 3 cells x 30A =~ 300 watts.
This is liable to be acceptable in many drills.
What your drill requires can be determined by operating it from a variable voltage power supply and measuring loaded current.
In the absence of a suitable power supply a well charged good condition 12V lead acid car battery would be a reasonable source.
If current is well above the LiIon cells rated maximum current under load their use is &quot;risky&quot;. If maximum current is under say 30A (which is likely) then suitable rated liIon cells are acceptable.
Charging MUST be carried out with an appropriate LiIon charger (not just a BMS) plus the use of an appropriate BMS is &quot;a very very good idea&quot;.
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Molicell (and some others) make 21700 size cells (eg Molicell INR-21700-P42A cells) rated at 45A continuous. If you can fit 3 of those in the drill it should meet any need.

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