CTO is not allowed to book leisure travel, so when you do LICWO, you are cleared hot to self procure airfare. However, you will only be reimbursed up to government constructed cost of your TDY trip. So, go on delta.com, purchase whatever you want, upload your delta receipt to DTS, AO approves, finance reimburses up to city pair amount.
It really is that easy. I've used CTO for probably 1-2 TDYs out of my last 15, no shit.