Do you know the voltage of the original battery? You can probably assemble something which will do the job by stacking a couple of "button" batteries together, and if necessary, pack out the extra length using alfoil or a small spring (such as in a retractable ballpoint pen), being careful to not short out against any metal on the sides of the battery receptacle. Eg wrap the circumference of your assembled battery with tape to hold it together, and to give it the right diameter.
Hope this helps!
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