There isn't an etymological link. "Shall" and "will" have different historic roots, which both can be found in Old English as "sceal" and "wyllan".
The etymology for "shall" goes back to Old English "sceal", which describes an obligation to do a thing. If you shall go to work on Monday, you shall because you must out of obligation.
The etymology for "will" goes back to Old English "wyllan" (also "willan"), which describes a desire or a wish. If you will go to work on Monday, it's because you want to go to work on Monday.
These meanings in general have not carried through to the modern day. Today, "shall" and "will" can be used interchangeably by way of the third definition of "shall" and the third of "will" as offered by Meriam Webster Online as "used to express futurity", though "shall" in particular is less common in colloquial American English than in British English. "Shall" also appears more commonly in legal writings written in both British and American English than in common literature.