Let's first look at mage hand (PHB 256). This is a spell which, when active, allows you to:
You can use your action to control the hand. You can use the hand to manipulate an object, open an unlocked door or container, stow or retrieve an item from an open container, or pour the contents out of a vial. You can move the hand up to 30 feet each time you use it.
So, here is my reading. This is granting an action called "control the hand", same as any other action. When you choose this action, you can "use" the hand to perform one of a variety of tasks. Additionally, as part of the same paragraph granting this action, when "using" the hand it may be moved up to 30 feet. By being in the same paragraph and echoing the same verb "use" as the previous sentence, this movement should be read as a direct effect of the action, and not as a triggered effect.
Mage Hand Legerdemain
Let's now examine Mage Hand Legerdemain (MHL, PHB 98). This is important, because this ability is worded in order to specifically enhance mage hand:
... you can perform the following additional tasks with [the hand]:
Additionally, it also modifies Cunning Action (CA):
In addition, you can use the bonus action granted by your Cunning Action to control the hand.
So why is MHL important to this question? Because it provides evidence of a very specific language that is used when the authors wish to modify an existent action. MHL grants "additional tasks" with the hand, not "additional actions". And when it modifies CA, it specifically calls the action "control the hand", which is the exact language used in mage hand to label the same action.
So, at this point, you have a single action, "control the hand". Due to MHL, this "control the hand" action may be used as a bonus action under CA. There are a variety of tasks which can be performed when you use this action, some granted by mage hand and some by MHL. Additionally, when you use the "control the hand" action, you can move the hand 30 feet.
Finally, let's examine Versatile Trickster (VT, PHB 98). This ability reads completely differently from MHL, which is on the very same page. Specifically, it grants a new bonus action, which is unrelated to the "control the hand" action and Cunning Action. Why do I know this? Because MHL shows the language they use to modify the "control the hand" action, and VT does not use that language. It does use the same language used to grant a new action to a player.
So, what does this new action do? It allows you to:
designate a creature within 5 feet of the spectral hand created by the spell. Doing so gives you advantage on attack rolls against that creature until the end of the turn.
Well, that doesn't sound like a new "task" for the "control the hand" action, does it? It sounds like a targeted ability. What happens when we select this target? We gain advantage. Interesting; no mention of the "control the hand" action nor of Cunning Action in relation to this action. (Remember, it's CA that allows you to use the "control the hand" action as a bonus action.)
Thus, my reading is that VT is granting a new bonus action that is separate and distinct from the "control the hand" action. And, since moving the hand is directly tied to the "control the hand" action, this separate action granted by VT does not allow you to move the hand.