definitely conversion has some cost whether it is explicit or implicit. and if the cast/convert have been used in left part of filter (like cast(last_name as nvarchar(30)) = 'bhuv') then it will also hamper the index usagel.
second , why you want to replace the code with cursor ? it wil definitely has some bad impact.
Post your code , for better opinion.
-------Bhuvnesh----------
I work only to learn Sql Server...though my company pays me for getting their stuff done;-)