Despite the fact that Sergey brings up in his comment to your question, the task is still very tough to be performed for an actively used application. I would assume that you meant to say, "SHA1" hashing algorithm. Encrypting using SHA1 would be as if you only want encrypt, and not decrypt.
Now, the thing is, that your passwords are hashed using SHA1 algorithm, keep it that way! Even if you want to upgrade your systems to SHA2 based algorithms, your users won't be happy. Due to many reasons:
1. You cannot change their passwords on your own, because you cannot revert the hash. If you knew their passwords, then the purpose hashing is unknown.
2. Their would be a conflict between password hashing of both the types. SHA1 and SHA2.
3. SHA2 is also going to fade away (as in your calculation!),
SHA-3[
^] is coming in hot.
Now, to answer your problem here. There is only one thing you can do, ask your users to update their passwords! It would be same as "updating" the passwords, once they have forgotten it. But only this time, you will allow them to enter their previous passwords as a security concern.
1: Updating the application's architecture, without prior and proper understanding of the side effects. I won't go up with updating just web.config to overcome this problem.
2: You would need to hold SHA1 digests for your current users and manage SHA2 digests for the rest. What I would suggest is that you create an extra field to hold "IsSHA2" and then check either one of them.
Otherwise, you can ask your users to update their previous passwords and update them to SHA2 digests.