@Doctor G
Harris,
Based on what you have told us, I don't see any problem with what you are proposing to do.
Just a caution though ...... The combined length of both barrels together is just over 4" ... that's a pretty long sweep for your tool. . So, if you did want to make the pen "parallel-sided", you might have a little difficulty keeping the cutting tool at the same distance from the turning axis over the whole 4" length.
You used the words "making it thicker", so perhaps you have in mind to put a slightly bulged profile on each half of the slimline.
Or perhaps you have something else in mind.
So, without there being anything present on your mandrel to indicate the center point, you could get the two halves somewhat different shape.
Oh ... one other thing ... you used the word "micrometer" for your tool to do the measuring ... did you mean to say "caliper" ?
Both will work, but a "caliper" is what most of us use .... there is a difference in how you handle these two measuring instruments.