To illustrate my situation I'll use some example keywords.
My website ranks well for the keyword 'dining chairs'. To my surprise it also ended up ranking for the word 'chairs'. Also one of the inner pages ranks well for wooden chairs. But I found out that a lot more people search for 'woodenchairs' instead of 'wooden chairs' and unfortunately I'm not ranking at all for 'woodenchairs'.
Now my question is, should I make backlinks to the page about 'wooden chairs' with the anchor text 'woodenchairs' or would it be better to make a new page and optimize it for 'woodenchairs'? I'm somewhat worried that I'll somehow screw up my rankings for 'wooden chairs'.
I don't see anything truly wrong with either approach. If you can create another page of valuable and unique content, then a new page can work - and you can croww link it with the existing page. If you really would be stretching things to come up with another uniqe and valuable page of content, then getting a backlink or two with the exact anchor text is fine.
But definitely don't overdo it on the arranged backlinks. THAT, rather than the spelling, could cause troubles.