As long as the wires are fastened to the connectors with screws or some type of quick connect/disconnect arrangement, this shouldn't be a complicated process.  It would only be scary if you didn't unplug the stove first . . .

Refastening wires to burner blocks was an occasional job on my mom's '49 Westinghouse, particularly on the only 8" burner the stove had.  There was very little slack left on that wire by 2008 when I shipped the stove to a former AW member.

Bake and broil elements can be made to order if needed, and they're not expensive.  You just have to go through an independent appliance parts retailer so they can match it up.  My mom's stove was on its third bake element when I shipped it off (she was an avid baker).  It sounds like the element from your parts stove could be the original type and may use coiled nichrome for its heat source instead of a modern infrared tubing.  If so, I think it should pop right in, and if it works, use it!