Hate to be the first to say it but that RCA unit is very inadequate for your Khorns. Not in terms of power as a 3 watt amp will drive you out of the room with the sensitivity of your speakers.
If you really want to do them justice, do a little browsing on the forum for recommended amplifiers.
I wouldn’t worry about the dust, but I’d recommended unscrewing and tightening all the input/output screws that you can see. This will help give a much better signal path between all the components.
If you want to use the RCA to just test it out, connect speaker wire to the RCA’s L and R outputs on the right side of the picture you posted them to the input connections of your speakers.