And yet there's all those beach cruisers running around with only a rear brake and very few front brake only bikes. I say turn it into the aeroist beach cruiser ever!Running just a rear brake on a single speed is a poor idea. Having just a front brake would be better. Your braking efficiency is roughly a 70-30 split. It would be different if you set it up as a fixed gear as you could use your legs for braking.
Does the bike have horizontal drop outs?
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Use a chain tensioner designed to single speed a MTB to handle the chain slack from vertical dropouts.