안녕하세요.
우선 "우윤히" --> "우연히"가 맞습니다^^
아마 아는데 '실수로' 저렇게 적은 것 같습니다. You probably knew it, but wrote that way 'accidentally.' :)
I accidentally deleted the address.
(저는) 실수로 주소를 삭제했습니다.
I accidentally fell asleep.
(저는) 어쩌다/어쩌다가 잠이 들었습니다.
You can theoretically say 실수로 잠이 들었습니다. or 우연히 잠이 들었습니다.
But they all imply different things.
실수로 implies that you yourself made a mistake, and even though it was an accident, there was still active involvement on your part.
어쩌다 or 어쩌다가 can actually mean 'how' as a question word (usually 'how' in a surprised or negative sense).
eg) 어쩌다 다쳤어? How did you hurt (yourself)?
As an adverb, it means 'accidentally' but also 'casually' or 'incidentally'. The focus is not on the active involvement of the agent, and whatever happened does not even need to be a mistake or something bad. Often you can render the translation as '(somehow) it just so happened/ended up/turned out that...'
That is why I translated the 'accidentally fell asleep' with 어쩌다/어쩌다가 because falling asleep is more out of one's control. But you can of course translate it as '실수로' if you want to emphasize the mistake of the agent who had the responsibility to stay up.
Likewise, you could say 어쩌다/어쩌다가 주소를 삭제했습니다. for the first example. However, this seems like you are trying to de-emphasize your own fault in an attempt to make your mistake more excusable. Using 실수로 sounds like you are more directly admitting your guilt. However, they ultimately mean the same, and some Koreans may feel differently about those nuances.
Finally, 우연히 really means 'by luck/by chance.' There is absolutely no sense of blame/guilt/mistake in this phrase. It is most often used with the verb 'to see/meet/run into': 보다/만나다.
My tip is, when in doubt, use 실수로 when an unintended result occurred. It is probably the most common adverb for such situation.
Hope this helps.