There's no such thing as a CP437-encoded String in [Node]JS. Strings are always Unicode (well, UTF-16 code units).
What you have in ¨Quin ha enga¤ado is String that has been decoded from bytes using the wrong encoding at some point in the past (aka mojibake). You need to find where that String came from, and change the encoding that was used to convert it from bytes.
It is sometimes possible to rescue a badly-decoded string by encoding back to a Buffer using the same encoding as was wrongly used to decode it, and then decoding it again with the right encoding this time. But this only works when all the bytes used happen to have mappings in the wrongly-used code page, and there is no further damage to the string.
It looks like you have a string that has been decoded using ISO-8859-1, so in principle you could encode it as ISO-8859-1 (eg new Buffer(s, 'binary')) and then decode the buffer as cp437 (unfortunately this encoding is not available in Node so you need a third-party module such as iconv-lite).
However, your string has suffered further damage in that the é has completely disappeared. That could be because the misdecoded character for that byte is an invisible control character that StackOverflow doesn't allow to be posted, or it could be because the that control character has been lost somewhere up the chain. If so, you cannot recover the original string at all.
I wish to dynamically detect the encoding type
There is no general way to automatically detect the encoding of a buffer, only vague heuristics (see the chardet module for an implementation of this). This is doubly difficult when you have mojibake, because you have to guess both the real encoding, and the wrongly-applied encoding.
You can burn a lot of time trying to detect common patterns but ultimately you will never have a reliable solution. After all, ¨Quin ha enga¤ado is a perfectly valid sequence of characters already, how would your code know that wasn't what was meant?
Much better to fix the bug further up, where the bad decode actually happened.