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Clipless is loads of fun! Makes stopping when brakeless much easier as well. I'm sure you could find a second hand pair of shoes and pedals cheap in the classifieds on here! Mountain bike shoes like spd or time atac are much better for still being able to walk around in than road shoes like SPD-SL or look. Either way, I wouldn't ride brakeless with only one pedal strap, it'd be a shame to crash a nice bike like that!
I'm the same. Maybe you should try clipless? You need proper foot retention if you're riding brakeless!