Reddit reviews Retro-Bit NES Classic - Adapter - NES Classic to Original NES Adapter (Retro-Bit) - NES;
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Compatible with NES Classic Edition/Wii/Wii UCompatible with Original NES and Retro-Bit Retro 8 Pro Controllers4 Inch extended cable
If you get adapters and plug in the NES Classic to a CRT, maybe. I'm assuming you already have the Duck Hunt ROM loaded on the NESC. It won't work on an LCD or (O)LED TV because light guns can only read from a CRT. You'll need a CRT if you wanna make it work.
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Here's some Amazon links:
HDMI to Composite Converter
NES to NES Classic Adapter