What is the safest way change my installation path URLs for my site.

This is quite simple actually. First off, log into the admin area and in the General Settings change area change the WordPress Address and Site Address to the root domain (iroywebdesigner.sg).

http://codex.wordpress.org/Settings_General_Screen

Then cut and paste (move)all of the files in your /wp/ folder to your domain name’s root folder. If you have a web host with cPanel this should be a simple drag and drop operation after you select all files and folders in the /wp/ folder. You can read more here:

http://codex.wordpress.org/Moving_WordPress
http://codex.wordpress.org/Changing_The_Site_URL