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Does your battery box include some circuit? I bet it has a resistor to set the overall current for the string, probably at about 20mA (2mA per LED). It may have an actual current limiter IC to do this, or a resistor.

Either way, without knowing what's in the box, you could just limit the gross current delivered to the whole string to the same as what a fresh set of batteries delivers.

How to make that? Well, here's an answer (simulate it here):

Design procedure: Measure the current off the battery, adjust the limiter current sense to achieve that target value. The design shown delivers about 18mA at 5V, you could use it just like that.

Or play around with a series resistor, like they did here: Calculating forward voltage for a string of fairy lights: multimeter shows "1" Back-of-the-book answer: they chose 85 ohms.

Does your battery box include some circuit? I bet it has a resistor to set the overall current for the string, probably at about 20mA (2mA per LED). Or it may have an actual current limiter IC to do this.

Either way, without knowing what's in the box, you could just limit the gross current delivered to the whole string to the same as what a fresh set of batteries delivers.

How to make that? Well, here's an answer (simulate it here):

Design procedure: Measure the current off the battery, adjust the limiter current sense to achieve that target value. The design shown delivers about 18mA at 5V, you could use it just like that.

Or play around with a series resistor, like they did here: Calculating forward voltage for a string of fairy lights: multimeter shows "1" Back-of-the-book answer: they chose 85 ohms.

Does your battery box include some circuit? I bet it has a resistor to set the overall current for the string, probably at about 20mA (2mA per LED). It may have an actual current limiter IC to do this, or a resistor.

Either way, without knowing what's in the box, you could just limit the gross current delivered to the whole string to the same as what a fresh set of batteries delivers.

How to make that? Well, here's an answer: LED supply 5-30 V - Zener diode?

Design procedure: Measure the current off the battery, adjust the limiter current sense to achieve that target value. The design shown delivers 18mA at 5V, you could use it just like that.

Or play around with a series resistor, like they did here: Calculating forward voltage for a string of fairy lights: multimeter shows "1" Back-of-the-book answer: they chose 85 ohms.

Does your battery box include some circuit? I bet it has a resistor to set the overall current for the string, probably at about 20mA (2mA per LED). It may have an actual current limiter IC to do this, or a resistor.

Either way, without knowing what's in the box, you could just limit the gross current delivered to the whole string to the same as what a fresh set of batteries delivers.

How to make that? Well, here's an answer (simulate it here):

Design procedure: Measure the current off the battery, adjust the limiter current sense to achieve that target value. The design shown delivers about 18mA at 5V, you could use it just like that.

Or play around with a series resistor, like they did here: Calculating forward voltage for a string of fairy lights: multimeter shows "1" Back-of-the-book answer: they chose 85 ohms.