Two sentences:
1, you have woken, but you didn’t want to wake him
Tee-widdi deheena, on dotty thimon moin ee-thiheen-o-vey.
2, You said that you had woken, but you didn’t want to wake him.
Wed-eyes-tee de-vod-ee widdi dheena, ond naga-teen moin ee-thiheen-o-vey.
Why “nagateen” in the second one, in stead of “dotty thimon”? Is it because “boad” was used in the first part of the second sentence?
Hi David! Unless someone knows better, I would just say they are alternatives and you can choose which one you like to use. That’s how I see them anyway 
Hi David, I’m confused a bit by your phonetic translation to the sentences, using the south version words, the first sentence translates to: (Rwyt) ti wedi dihuno, ond doeddet ti ddim (d’'ot’m) moyn ei ddihuno.
The second sentence can be, Wedest ti dy fod wedi dihuno,ond doeddet ti ddim (d’ot ti’m) moyn ei ddihuno.
Nage is a negative in a different context. Hope that you find this helpful.
I really, really don’t want to get involved in this level of Welsh, but seeing as few other people have, here goes - (deep breath…;-))
Echoing Dee, I hope someone who knows about such things answers, but til then…
“Nag” is used in Iestyn Welsh for the “that” negative, so when you say
“Is it because “boad” was used in the first part of the second sentence?”
I think you are correct.
Basically, “you said that you had woken, but you said that you didn’t want to wake him.”
Rather than the two phrases being unrelated, if you see what I mean.
Now, Iestyn Welsh uses “nag” rather than “bod…ddim”, if you see what I mean.
So therefore, the meaning of “you said that you had woken, but you said that you didn’t want to wake him” can be translated as
Wedest ti dy fod ti wedi dihuno, ond nag o’t ti’n moyn ei ddihuno fe.
[nag can be used in other ways, including a straightforward negative as Dave says, but I don’t think Iestyn uses it this way on SSIW.]
Now, the above may be complete nonsense, just saying that I myself understood your writing of the Welsh, and that I don’t think Iestyn shortens “dim” to,“m” (at least, not on SSiW!)
This is the sort of stuff I would be asking other people about, so please do not take what I say as instructive in any way!
Owain’s explanation makes sense. Diolch.