Using single quote in an Exec statement in SQL

I am having issues executing a SQL statement from a stored proc having single quotes. Here is my query from a stored procedure that I am executing.

EXEC('UPDATE myTABLE 
         SET myCOLUMN = (SELECT Replace('OSINGLEQUOTEJOHN DOE','SINGLEQUOTE','''')')

I am trying to update table "myTABLE" column "myCOLUMN" with a value "O'John Doe"

The actual query is like this, i tried to simplify it a bit in the above example

EXEC('UPDATE myTABLE 
         SET myCOLUMN = (SELECT Replace('+ @IntegrationGuardian2FullName +','SINGLEQUOTE','''')')

The value of @IntegrationGuardian2FullName is "OSINGLEQUOTEJOHN DOE". Hope that makes more sense.

Can any body help me formatting this query?