I don't think it's as simple as filling in blanks with corresponding sense words. I think there is also something to the usage of show in this question. For instance, in the first example, "play" functions similarly to "show".
- I want to show you something.
- I want to play you something.
But in the second example it does not:
- Can you show me?
- Can you play me?
This is because we can remove it and to with the verb show and not lose the meaning.
- Can you show me?
- Can you show it to me?
However, it should be noted that the unspoken it or something in "Can you show me" is the direct object of the sentence and me is the indirect object. Without the it/something, ambiguity exists. A similar sentence could be written where me is the direct object and there is no indirect object:
"Which one of you dolls should I show to Mrs. Claus tonight? asked Santa."
"Can you show me? asked Betty the Doll."
This omission is not always possible. Play does not function the same way as show though. We cannot remove it and for and retain the same meaning.
- Can you play me? (Something a talking instrument might ask)
- Can you play it for me? (A request to hear something)
A closer meaning to OPs example would be "tell", which works identically in both cases:
- "I want to tell you something."
- "Can you tell me?"
However, tell only covers speech.
The combinations of verbs with dependent prepositions are vast in English; and it's not necessarily that we lack a verb to fit a specific construction, but that just because some verbs share a common trait (i.e. they deal with senses), they don't necessarily share a common construction. To show vs. To play is an example of this. With that said, all five sense words (taste, touch, see, smell, hear) can form identical constructions.
- I want you to taste something...Can I taste it?
- I want you to touch something...Can I touch it?
- I want you to see something...Can I see it?
- I want you to smell something..Can I smell it?
- I want you to hear something...Can I hear it?
