I presume you wish to hide behind a creature using human shadow and then climb that same creature using limb-climber? If the first part is successful, then the creature would be denied their Dexterity bonus to their CMD* for the purposes of using limb-climber to climb said creature. The attempt would also break Stealth once resolved. Other than that, there appears to be no interaction between the two abilities.
*There has been discussion on whether this is actually true; feel free to read and draw your own conclusions.
Limb Climber has some holes in it. For one thing, it isn't exactly clear what square you are in, although I think you share the climbee's space (like a mount).
Assuming that is true, the creature you are climbing can provide you cover to make a stealth check which is what human shadow allows. Regardless of whether you have human shadow or not, the creature will provide soft cover from attacks.
Vexing Dodger tells you what penalties, the climbee takes a penalty to attack roles against you equal to the number of sneak attack dice, that is it.
You will get a +4 on your AC for others trying to attack you, due to the climbee giving you soft cover against their attacks.
No one gets any bonuses from this alone (although if you stealth and sneak attack someone the normal bonuses for that apply.)