catch-22
If you could attach Sram links to the ends of the Shimano chain to use the Sram link, it would be just as easy to use the same system to close the chain.
I don't know if Sram makes a wider link, but a few others might. In any event Shimano does make narrower chains, and that might be the answer for you. The other, simpler, option is to buy a KMC or Sram chain which already comes with a matching link.
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