You might need to think about the context of this conversation. However, the following is my simple guess: でしゅ comes from です and very small children say like that. (It's kinda hard for them to pronounce です) So, でしゅ/でちゅ is a typical word to behave like a small child.

These are hypocorism/baby talk. ”俺でしゅ” ”俺でちゅ” ”私でしゅ”　”まんま” 「ねんね」、「あんよ」、「ぽんぽん」 etc...