As I understand it, the Greek does not say touch or hold, it says “cling”.
Cling is a more permanent touch; that would be a middle voiced perfect tense; but the passage in John doesn’t have that. On the other hand, I think your interpretation is about as solid as anyone elses on that particular spelling in John … I personally haven’t figured it out yet !
He did not want others clinging to Him because He was leaving them again. Even in His case, when someone has died, we do not get them back, not in the original relationship that once existed.
Touching is ok, viz: Thomas. Clinging and holding, however, seek a physical relationship that was gone (or one that would not exist until Heaven).
The particular word and spelling used in John 20:17 is rather unique.
Touch is not spelled exactly that way anywhere else in the bible, NT or OT.
A typical example of spelling “touch” in Greek is found in Psalm 104:15:
Psalm 104:15 μη
απτ-εσθε των χριστων μου και εν τοις προφηταις μου μη πονηρευεσθε
Psalm 104:15 Touch ye not my anointed: and do no evil to my prophets.
The word is used in three general kinds of contexts throughout scripture:
When an item was exceedingly valuable, or dangerous; In that case handling it (or even touching it briefly), was a taboo out of fear.
This includes people’s wives (pharaoh vs. Sarai), belongings (Sinner tribes and their incense in the desert…, The fruit of a certain tree in Eden ), dead bodies of people and animals, etc., and even very clean but ritual/holy items (a newly sanctified altar.)
The third way the word is used is to mark out a boundary, or an extent, that something may “reach” to. One long curtain may reach, join, or “touch” it’s neighbor; Often enemies would touch together on points that they agree on (join together.); but says something like “they touch together” (meaning act together…), etc.
The context in John has several elements:
The angels have spoken Jesus’ words to Mary Mag., and there is no one else around to have witnessed the accounts we read in scripture. Mary, herself, then must have told the apostles the words that were said – and admitted that she did not understand/believe these people to be divine angels in a clear mind.
Rather, she admits being confused and told the angels that she
wants the body.
Which she came, specifically, to finish handling for BURIAL. Eg: she came to finish embalming it.
When Jesus repeats the exact same words the angels have spoken (or rather, that HE spoke through them), notice in the account – she does not recognize him
EITHER; she CONTINUES to seek a dead body.
However, when Jesus finally uses her NAME, then (and only then) she recognizes him – and it is immediately followed by a cryptic prohibition that may or not be against “touching” him.
That connection and the stubborn-ness of her believing a body is to be buried suggests that she may still be thinking “Is this really a dead body I am talking to that needs to be buried?”
The reaction, then, is: Whoa, there, Mary – I don’t need more bandages and slime; I haven’t finished dying yet.
In any event, the Greek spelling in John 17 is mildly problematic:
What John has is:
John 20:17 λεγει αυτη ιησους
μη μ-ου απτ-ου ουπω γαρ αναβεβηκα προς τον πατερα πορευου δε προς τους αδελφους μου και ειπε αυτοις αναβαινω προς τον πατερα μου και πατερα υμων και θεον μου και θεον υμων
The first bold word is a negation; “mE” which is used for reversing the sense of a
verb or an “ing” word…
However, the next word “mou” is not a verb or an “ing” word…
Rather it is the word of possession or ownership (eg: – of-me / mine – a “genitive”) That is followed by a word which NORMALLY would have a verb ending…
At first glance it looks Genitive (in agreement with the previous word.); but if we take it to be a verb ending – it would just about have to be a word in the “second person Imperfect Middle voice”. However such a tense and voice expects an extra letter (an augment) to be added to the word – “touch” – and the prefix simply is not there. Since there are no other examples I can check this with, though, there is no way to determine if this spelling in John is a mistake – or just a convention for that particular word

.
Assuming the voice/tense is still correct – Jesus is telling her about an event that happened in their mutual past – but is NOT happening Now.
Jesus, then, isn’t saying “don’t keep touching me…”; Rather his thought is along a subtly different line…
“Before, You yourself, of-me couldn’t touch; for not-yet I have-ascended-perfectly to The Father”
There are some issues with double negations, and how to harmonize the sense of the passage … but I can’t solve those now; I don’t know enough.
There are also additional minor grammatical oddities; eg: “The” is not dative, but accusative. In any event, the sentence is about a reversal in ability to touch something belonging to Jesus. (his body?)
Contrast it to another place where the SAME ROOT word for “touching” is used:
Luke 7:39 And the Pharisee, who had invited him, seeing it, spoke within himself, saying: This man, if he were if a prophet, would know surely who and what manner of woman this is that
toucheth him, that she is a sinner.
Luke 7:39 … η γυνη ητις
απτ-ε-ται αυτου οτι αμαρτωλος εστιν
Luke 7:48
And he said to her: Thy sins are forgiven thee.
Luke 7:49 And they that sat at meat with him began to say within themselves: Who is this that forgiveth sins also?
Luke 7:50 And he said to the woman:
Thy faith hath made thee safe. Go in peace.