I have never heard of the idea of a 'magnet flying past a coil really
quickly' to generate a spark. Imho there is a hall sensor in there or a
transistor circuit that does something or other to shape the pulse when
the field is maximum. If you can find this, then you will be able to tap
into it at low voltage.

Another way is to add a small insulated winding of your own (1-10 turns)
and short it out with a relay or a mosfet. The shorted winding will shield
the magnet's field and there will not be enough energy to spark (I hope).
This used to work with small motors whose points were impossible to
access safely.

Peter

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