Throwing and throwing or throwing back and error message

I have a static method in a utility class that assigns a value to a field.

Cutting version of my method:

public static void assignValue(String field, String valueToAssign){
    ...
    //code to do assign
}

If there is an error, I am currently throwing an exception, but I'm not sure if this is the right approach, because I am calling assignValuein a loop, and I want the loop to continue even if there is an exception. Therefore, you can potentially eliminate many exceptions.

for(int i = 0; i < assignmentList.size(); i++){
try{
    assignValue(assignmentList.get(i).fieldName, assignmentList.get(i).fieldValue);
    }catch(AssignmentFailedException e){
        errorlist.add(e.getMessage());  
    }
}
}

Would it be better if you assignValuereturned an error message instead of an exception? Then I can save the error and throw an exception when the list is complete.

for(int i = 0; i < assignmentList.size(); i++){
String errorMessage = assignValue(assignmentList.get(i).fieldName, assignmentList.get(i).fieldValue);
if(errorMessage != ""){
    errorlist.add(errorMessage);    
}
}

If I go to approach the error message, should I rename this method so that users know that the error message will be returned?