I like the sound of
Henry Erik and
Henry Karl, and the vintage vibe of
Henry Wilfred,
Henry Arthur and
Henry Alfred.
Edward and
Emmett repeat the e sound in
Henry in a way I don't much enjoy, though
Erik doesn't bother me in that way for some reason. I would avoid
Henry James, partly because
James has become such a knee-jerk reflex choice as a mn but mostly because I find the novelist unappealing: so long-winded, and when he finally gets to his point, I've usually forgotten why he needed to in the first place.
I think I'd choose
Henry Wilfred, because it's surprising and exciting, and
Wilfred is a family name anyway.