I'm not an expert but it will be a lot easier if he is found and signs.
Also depends a bit on whether country has strict sole guardianship and your spouse has that.
Some options that may help or in some cases work but may depend on country and laws about guardianship etc:
-can certainly write a letter of explanation that his whereabouts are not known. On its own I think chances of this being enough are low - but you could submit app and get prepared for the (inevitable) procedural fairness letter / request for something like proof of sole guardianship.
-Same but add eg affidavits of any proof that whereabouts not known, search has been thorough, and spouse has not exercised parental rights or duties in xx years. (Better but possibly still not enough)
-Go through court process to declare spouse as sole guardian etc because spouse has disappeared. That may take time depending on country.
Hope this helps but again, a lot easier if spouse is found and signs.