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Is what I currently came up with but I think it is much to direct.
I want to express something like this:
"I would be very pleased to find a Japanese language exchange partner" (meaning a male or female, native speaker)
I would say
「日本語を教えてくださる方を探しています。代わりに英語(or French or Russian? I don't know what your mother tongue is.) をお教えします。男性でも女性でも構いません。」
Required, but never shown