It uses Charisma
The operative phrase is "as though you were not incorporeal."
Any creature that becomes incorporeal has no strength score (SRD, Incorporeal Subtype):
It has no Strength score, so its Dexterity modifier applies to both its melee attacks and its ranged attacks.
On the Material Plane, but not on the Etheral, a ghost is incorporeal, so it follows that it never has a Strength score while on the Material Plane (SRD, Ghost, Emphases mine):
Manifestation (Su): [...] When a ghost manifests, it partly enters the Material Plane and becomes visible but incorporeal on the Material Plane. [...] A manifested ghost remains partially on the Ethereal Plane, where is it not incorporeal. A manifested ghost can be attacked by opponents on either the Material Plane or the Ethereal Plane. The ghost’s incorporeality helps protect it from foes on the Material Plane, but not from foes on the Ethereal Plane.
Corrupting Touch (Su): [...] Against ethereal opponents, it adds its Strength modifier to attack and damage rolls. Against nonethereal opponents, it adds its Dexterity modifier to attack rolls only.
Draining Touch (Su): [...] Against ethereal opponents, it adds its Strength modifier to attack rolls only. Against nonethereal opponents, it adds its Dexterity modifier to attack rolls only.
You can see that the "[...] Touch" abilities use the same rules as the incorporeal subtype for attacks. So, on the material plane, a manifested ghost is incorporeal and thus has no Strength score.
The Rules for Corporeal Incorporeality
Libris Mortis, page 143 has a section on "Losing Incorporealness" Which says, in regards to a Strength score:
The now-corporeal creature gains a Strength score equal to its Charisma score (not including any nonpermanent modifiers to Charisma, such as an eagle’s splendor spell). Its incorporeal touch attacks become normal touch attacks (and it uses its Strength modifier on attack rolls unless it has Weapon Finesse).
A ghost, or any incorporeal creature, using the benefit of ghostly grasp to 'wear, wield, and otherwise use corporeal items as though [it] were not incorporeal', would 'lose incorporealness' relative to those objects and have a Strength equal to its permanent Charisma in regards to those objects.
Rules Compendium p. 64-5, under the "Attacks" heading, has a similar rule for incorporeal creatures interacting with other incorporeal creatures, and rules about not being able to interact with corporeal creatures:
An incorporeal creature can’t trip or grapple, nor can it be tripped or grappled. In fact, it can’t perform any physical act that moves or manipulates a corporeal opponent or that foe’s equipment, nor is it subject to such acts. An incorporeal creature that attempts to grapple or move another incorporeal creature or object uses its Charisma modifier for rolls on which a Strength modifier normally applies.
Ghostly grasp, in permitting the use of items (objects), permits the incorporeal creature to ignore the "or that foe's equipment" clause, and interact as if corporeal with it, such as attempting to disarm them, using Charisma where Strength would otherwise be used.
Additionally, for creatures that wear clothing and/or armor, the incorporeal creature might even be able to trip or grapple them. Or even try to catch them when they're falling...