Good word for something physical that's inexplicable

There's really nothing unusual about a thing that can be perceived by touch and by no other sensory experience.

Objects can be perceived variously by one or more, or none, of the sensory feelings. There are colorless, odorless and tasteless things that can still be 'felt' through other means.

Certain gases are highly corrosive and can cause an immediate sense of discomfort, yet cannot be "felt" by the senses.

A (hypothetical) substance can exist that can be felt by touch (tangible), yet not visible: The tangible.

Static electricity is invisible, odourless and noiseless but can be felt, both indirectly (it can make the hairs on your body rise) and directly (it gives you an electric shock when a sufficient potential difference exists between you and an adjacent object).

By the way, your question is self-contradictory: if you can feel something, it is not imperceptible.

The wind is invisible, yet tangible.

It's invisible because it doesn't absorb light that we can see with our eyes. But it's also tangible because we can perceive it by the sense of touch, e.g. a morning breeze on one's cheeks.

tangible: capable of being touched; discernible by the touch; material or substantial.

I would call them tactile qualia. Tactile means relating to the sense of touch, and qualia is a more general term for what you are asking that is not limited to the sense of touch, but could also be a smell, or a sight, or etc.

If you absolutely need a single word, I think the term qualia expresses the most important aspects of what you are after.

From Wikipedia:

Qualia is a term used in philosophy to refer to individual instances of conscious experience. The term derives from a Latin word meaning for "what sort" or "what kind." Examples of qualia are the pain of a headache, the taste of wine, or the perceived redness of an evening sky.

Daniel Dennett identifies four properties that are commonly ascribed to qualia:

• ineffable; that is, they cannot be communicated, or apprehended by any other means than direct experience.
• intrinsic; that is, they are non-relational properties, which do not change depending on the experience's relation to other things.

• private; that is, all interpersonal comparisons of qualia are systematically impossible.

• directly or immediately apprehensible in consciousness; that is, to experience a quale is to know one experiences a quale, and to know all there is to know about that quale.

Ethereal

extremely delicate and light in a way that seems not to be of this world.

My suggestion:

Tangible phantom

Tangible: perceptible by touch. "the atmosphere of neglect and abandonment was almost tangible"

Phantom:

• a ghost. "a phantom who haunts lonely roads"

• a figment of the imagination. "he tried to clear the phantoms from his head and grasp reality" synonyms: figment of the imagination, delusion, hallucination, illusion, chimera, vision, fantasy, mirage;

• not real; illusory.

Some of the synonyms for phantom also works

Covert means secret or hidden. Soldiers might take part in a covert mission to infiltrate an enemy camp — and you might take part in a covert mission to steal your brother's leftover Halloween candy.

Covert is the opposite of overt, which means obvious, or in full view. Covert things are hidden, private, or stealthy.