Originally Posted by
Retro Grouch
What do your rear dropouts look like?
Unless they have a horizontal slot that the rear hub mounts to you won't be able to tension your chain. Now that you mention it, define for me what 10-speed means to you. 10-speed has come to have two very different meanings regarding bicycles and it makes a difference in the correct answer to your question.
With a bit of trial and error with different ring and sprocket sizes, it’s possible to find a gear close enough to what you want that won’t require tensioning.
That works better with an old wider chain, though; narrow 10spd chains don’t stand up to repeatedly taking links on and off to experiment.