4.5V power adapter is not sufficient to run your equipment. A 5V equipment must get at least 4.75V to run properly ( +/-5% tolerance).
If you are lucky, your 4.5V power adapter may run on the + tolerace side and output more than its rated voltage under load and runs your equipment properly. You have to test and see. With this small voltage difference, you do not encounter devastating electrical problems. After you make all the connections, including that of HDMI, and power on the devices, just observe all the devices for half an hour for malfunction. If you see video deformation on the HDMI-connected device, than switch everything off.
6V may be high for your HDMI converter. If you have the spec sheet of the device for which you need the power adapter, please check it. You may also go online to find information on your HDMI adapter.