there may be a kink

Use flat jaw pliers to straighten out any kinks. I've done this with resistor leads, headers, and card edge connectors.

 

How risky is it to bend the pins on a right angle header, to convert it to a straight header? Should I try it, or go right to buying a de-soldering iron and replacing the header? It is a wireless RF module, that fits my project case, etc... better if the header was straight in.

A good pair of needle nose pliers and gentle bending is how I would approach it. I could also drill the end of s chop stick and use it to gain leverage, maybe? or a piece of brass tubing, but I no longer have a source locally for this
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I dislike de-soldering with wick. I am successful at it, after a few attempts. It seems like a lot of work, that a de-soldering iron would eliminate. I have the straight header...

If straightening doesn't work for you, you can always opt for desoldering. Cut the leads leaving just enough to get a hold of with a pair of pliers then remove each pin one at a time.