Husband and wife apply to refinance their primary residence, shortly thereafter, the wife passes away, the husband re-applies on a different date. Would the original application date be used or the new one where the husband applied alone?

What happen with the first application? Was it denied, withdrawn, approved but not accepted.....?

It was approved.

The husband came back and completed a new application approximately a month later and the loan has originated; however, I am unsure of which application date to use - do I use the first one with both applicants or the 2nd one that originated with the husband only as the borrower?

So you have two applications and two separate entries on your LAR.
The first one for husband and wife was approved but not accepted. Use the date of the original application by both of them.
The second time the husband came in and applied by himself and you closed the loan. Use the date he came in alone and reapplied for this loan.