Male-male flat HDMI cable
At 10cm or less, you will most probably get away with using straight wires instead of twisted pairs. Even at full HD, your pixel clock will be 165MHz at most (less than USB2.0), and I have seen flat cables used for USB at such lengths. Also, there are commercial HDMI cables which use flat ribbon at the last few centimeters to enable easy termination.

To maximize your chances, make sure that:


each differential pair runs on adjacent wires inside the ribbon cable
differential pairs are separated by at least one shield wire to reduce cross-talk


As a side note, there are longer DIY HDMI cables out there, but those are usually based on a CAT-5 Ethernet cable which provides twisted pairs with suitable characteristics.

I'd also like to reiterate my comment: there are short HDMI cables for under $1, so honestly, your time will better be spent elsewhere.