I think it should be OK insha'ALlah, especially if you know your way around. Wear an abaya and you will be able blend in. Do you speak Arabic? If you do, you should be able to communicate well with the shop owners. Jeddah is a generally safe place. Of course it is always safer to have someone with you. Have a cell phone on hand just in case you need to call a relative to come and pick you up.
I think Br. akhan can provide more input on this.