Actually, this is a 2 part question.
Is it possible to use some sort of functionality to search through every stored procedure for a string and possibly rep
Stored procedures cannot be updated in place without first scripting them out as ALTER PROCEDURE statements (or DROP/CREATE, but I prefer ALTER PROCEDURE..more on that in a moment). The good news is, you can script all the procedures to a single file through SSMS. The DDL statements will initially be CREATE PROCEDURE, which you'll want to replace with ALTER PROCEDURE, along with your other changes.
While you could alternatively script the procedures as DROP/CREATE, I don't like doing this for a large number of scripts because it tends to cause dependency errors.
As for part 2 of your question, you'll need to edit any database path changes manually through the script.