Here are the lyrics from the Hermes Nye version as printed in accompanying booklet. I added some line breaks not in the original to aid in readability, and some comments in brackets to explain myself when needed, with my annotations being represented with *[#] while original annotations have just a * to mark them.
You can listen to Nye's rendition here.

DAVY CROCKETT
(As sung by Hermes Nye)

Well, don't you want to know something concarnin
Where it was that I come from and where I got my larnin?
O, the world is made of mud out of the Mississippi River,
And the sun's of all the forest fires*[1] as you may soon disciver.

Now, out one day, I was a-goin a-spoonin,
and I met Davy Crockett and he was a-goin a-coonin.
Says I, "Where's your gun," - "Well, I ain't got none" -
"How you gain to catch a coon when you ain't got a gun?"

Says he, "Pomp Calph, just foller after Davy
and he'll soon show you how to grin a coon crazy."
Well, I follored on a piece and thar sat a squirrel,
he was a-settin on a log and eat'n sheep sorrel.*

When Davy did that see, he says to me:
"All that I want now is a brace against your knee."
And thar I braced him, the great big sinner,
He grinned six times - hard enough to get his dinner.

But the critter on the log hit didn't seem to mind him,
just kep a-settin thar and wouldn't look behind him.
Then it was Davy said, "Well, the critter must be dead
you can see the bark a-flyin all around the critter's head.

Well, I walked right up the truth to disciver;
drat, it was a pine-knot so hard it made me shiver."*[2]
Says he, "Pomp Calph don't you begin to laugh
or I'll pin back your ears and bite you half and half.

Well, at that, I throw'd down my gun and all my ammunition,
Says I, "Davy Crockett I can cool your ambition."
But he throw'd back his head and he blow'd like a steamer,
Says he, "Pomp Calph, I'm a Tennessee Screamer."*

[this section spoken freely, line breaks added for long pauses]
"Yup" says he, "Now ain't I a rip-tail snorter, the yeller flower of the forest,
half-horse and half-alligator, that's me, with just a little tech of the earthquake thrown in;
clear meataxe disposition through and through; whupped my way through wildcats*[3] every mornin before breakfast,
all brimstone but the head and ears and that's aquifortice.
I can ride bare-back neked on a streek of lightning through a crabapple orchard and never get scortched or scratched.
Yes siree, I live on a rough street in a rough town, the further down you go the rougher it gets and I live in the very last house.
I rekin I can swim further, dive deeper and come up dryer than any other man in the district.
And if'n I ain't got the fastest horse, the ugliest dog and the prettiest sister in all Kentucky I hopes to be teetotaciously expluncticated."
So saying, he riz up, flapped his ears, whinnied like a horse and crow'd like a Dominiker rooster.

Then we locked horns and we wallered in the thorns;
I never had such a fight since the hour that I was born.
We fought a day and night and then agreed to drop it.
I was pretty badly whupped and so was Davy Crockett.

Well, then I looked all around and I found my head was missin;
he'd bit off my head and I'd swallered his'n.
Then we did agree to let each other be,
'case it was too much for him and he was too much for me.

Take the ladies out at night,
They shine so bright;
They make the world light
When the moon is out of sight.

*sheep sorrel: a plant found in dry places (principally in the east) with pleasant acid-tasting leaves.
*Tennessee Screamer: a "stout fellow".

--------------------------------------------------------------------

Comments on these printed lyrics from me:
*[1]: It sounds much more like Nye sings "And the sun's a boll of foxfire" rather than the lyrics printed in the booklet
*[2]: It would make more sense to end the quotation after "critter's head" rather than where it ends in the text.
*[3]: It sounds to me more like Nye says "I whupped my weight in wildcats" rather than the provided lyrics