tl;dr It is regional speaking, and former has emphasis on it where latter doesn't.
Here's what I found. This wording can be found in 三河弁. Although this is spoken in Aichi, I (from Hyogo) do speak this sometimes.
In this dialect, 〜や(あ)せん in the regular form is 〜や しない.
So わかりゃあせん in regular form is わかりやしない.
Now, わかりません vs わかりやしない(わかりやしません) is slightly different.
We'll break わかりやしない into words...
where や is very interesting. や is actually
Engagement particle は turned into casual speaking.
So that being said, this phrase is originally わかりはしない, whose basic meaning is "わからない". This は emphasizes preceding word. So it can be interpreted as "I(we)'ll never know."
What about わかりません? It's simply "I don't know," no emphasis put. That's the difference between them.