You got me curious, so I googled about this.
HERE is one article I found detailing a few studies that looked into side effects of vasectomy. Dates from 1995, and seems to be aimed mostly at athletes, having been published in
Muscle and Fitness magazine.
I found a page
HERE that lays out some other facts, including increased risk of cardiovascular disease. Though it goes into greater detail about the ramifications of sperm re-absorbtion, it specifically denies a link to hormonal changes or problems that might cause.
Finally I found
THIS ARTICLE which says, in short, not to worry about it: "Two common worries about vasectomy are that it will reduce a man's sex hormone levels or take away his ability to have sex. These myths have no biological basis, however, because vasectomy only prevents the escape of sperm from the reproductive system, not the release of testosterone, the male sex hormone, into the bloodstream. Both sperm and testosterone are produced in the testicles, but they leave by different routes. Sperm move through a series of ducts that channel through the reproductive organs to the outside of the body, while tiny veins in the testicles transport testosterone into the bloodstream."
You should probably be having this conversation with a doctor. They can assess your current health and give you a realistic prognosis and likelihood of side-effects.