Mryntu

I have heard in the past a kind of argument to show that there is no self along the lines of: are you your body? No, your cells regenerate all the time. Are you your emotions? No, they come and go. Are you ... ? The questioning goes on and on like that till there is nothing left. Is that argument actually found in the sutras? If yes, in which one?

Not-self (Anatta) is a teaching which is difficult even to understand by an advanced practitioner. Anatta Lakhana Sutta is the direct teaching of this doctrine.
https://www.accesstoinsight.org/tipitaka/sn/sn22/sn22.059.mend.html

You might want to read :

SN 12:15 • Kaccanagotta
https://www.dhammatalks.org/suttas/SN/SN12_15.html
https://suttacentral.net/sn12.15/en/bodhi

MN 72 • Aggi-vacchagotta Sutta
https://www.dhammatalks.org/suttas/MN/MN72.html

MN 109 • Mahā Puṇṇama Sutta
https://www.dhammatalks.org/suttas/MN/MN109.html

“He assumes feeling to be the self, or the self as possessing feeling, or feeling as in the self, or the self as in feeling. He assumes perception to be the self, or the self as possessing perception, or perception as in the self, or the self as in perception. He assumes fabrications to be the self, or the self as possessing fabrications, or fabrications as in the self, or the self as in fabrications. He assumes consciousness to be the self, or the self as possessing consciousness, or consciousness as in the self, or the self as in consciousness.

“This, monk, is how self-identification view comes about.”

It's in the The Questions of King Milinda, in the section which contains the analogy (or parable) of the Chariot.

Then, what is this "Nagasena"? Are perhaps the hairs of the head
"Nagasena?"

"No, Great King!"

"Or perhaps the nails, [etc.]

The questions, the Milinda Panha, is in the Khuddaka Nikaya.