Can you ‘inhapt’ an object (as a haptic alternative to ‘inspect’)?

Instead of saying that we investigate an object, we often use the verb ‘inspect’. According to my dictionary, the ‘in-‘ prefix is an intensifier and the ‘-spect’ suffix is derived from the Latin verb specere, meaning ‘to look at’, ‘to see’.
To ‘inspect’ then is more than just seeing or looking at something. It means to look intensely, carefully and closely.
This is of course what museum curators do all the time when they get new objects into the collections. They look carefully at the objects and often document the inspection by means of photography (or drawing or painting).
But sometimes curators investigate objects through other senses than vision. For example, they may touch and smell the objects, sometimes deliberately, or at least accidentally in the course of looking at it. They may even taste it.
In these cases, the verb ‘inspect’ is obviously insufficient, even misleading. For example, when I handle or finger an object to investigate its texture, its temperature, its dry-/wetness and its soft-/hardness, I obviously don’t ‘inspect’ it. I may do so in parallel with the handling and fingering, but the primary activity (handling, fingering) is not covered by the verb ‘inspect’.
Speaking in terms of ‘inspection’ when one listens, touches, smells or tastes an object intensely and carefully is an instance of what is sometimes called the ‘hegemony of the visual’. The unique experience of other senses are reduced to that of vision.
What verbs can be used for listening, touch, smell or taste objects intensely?
My dictionary doesn’t have any intensified synonyms of any of these sensory activites. One has to use phrases like ‘intense smelling’, ‘attentive listening’, ‘intensive touching’.
‘Intense touching’ has unintended erotic rather than curatorial connotations. So what about ‘inhapt’ (from Greek hapto, I grasp; cf. haptics) as a straightly curatorial term?
‘Inhapt’ isn’t in the OED and is also a clumsy combination of Latin and Greek. But it’s new and sounds nice: “I’m going to inhapt the new collection of plastic syringes today”.