Doubt when translating しかも and しかと in this excerpt

Question

I was reading an answer on Yahoo! Chiebukuro about Nichijou series. In the answer, the poster quoted an excerpt from a light novel Nichijou no Shousetsu. It's about a tale of Momotaro being played by Nichijou characters.

さて、さるをお供にしたももたろうが、元気良く鬼が島に歩いて行くと、その途中で、今度は犬が現れました。
「……!」
「……!」
しかも、戦っています。
しかと、戦っています。
いぬ役の校長先生が、役をほっぽり出して、しかと戦っています。校長先生、出番ですよー!
[中略]
「な、なんでしかと戦っているのー!?」
このおじさんが校長先生だと知らないももたろうは、あわてるばかり。
たしかに、街中でいぬとしか⁽¹⁾が戦っていたら、誰だってびっくりします。

I could understand the overall meaning, but having a doubt on bolded sentence. When I was reading it the first time, I translated the bolded sentence as:

然も【しかも】、戦っています。
Moreover, he is fighting.

確と【しかと】、戦っています。
Certainly, he is fighting.

However, when I reached (1), I realized that I might be mistranslating しか since 鹿【しか】 (deer) was more likely.

In the end, I translated them as

然も、戦っています。
Moreover, he is fighting.

鹿と、戦っています。
He is fighting with a deer.

One thing that made me doubtful was, as far as I know, there was no deer in Momotarou. However, I heard that there are alternative versions with different companies, so it might be just another variation that Nichijou created.

Also, I didn't translate しかも as 鹿も because it's the first time the deer was introduced, and there was no fighting introduced beforehand (in this excerpt).

Am I correct in translating those sentences? (I realized that the redacted excerpt might remove some important context, but it's beyond my control)

Answer 1

I think your translation is good.

I think this was played on a street where there were deers because the content says that いぬ役の校長先生が、役をほっぽり出して、しかと戦っています(The school headmaster is fighting with a deer, forgetting his part as a dog) and 街中で(on a street). This 鹿 would not be related to the content of Momotaro.