How to control sources and outputs? (asking for suggestions)

Hello! Here's a cute picture I made.

On the left is my current setup and it has the problem of having to disconnect cables every time I wish to change to listening with monitors. It is a possibility to ditch the Nuforce IconHDP and replace it with an oDac, as it might simplify things and simply be a better dac.

What would be the missing desktop-sized piece marked as ????? on the right? I realized it should have a pre-out for adjusting the volume on the speakers and having a good phonostage is a plus. I could get rid of my current phonobox and lose an extra component this way.

I was looking at some DJ-mixers but they seem a bit fiddly, big in size and quickly climb up in prices. Also I'm not sure if they would be able to switch between outputs.

I admit I have no idea what such a device might be called (router? switch?) and the fellows at the local audio shop were a bit clueless about what to do. (They don't do desktop audio that much)

Small

100-200€

able to pick inputs & outputs as neccessary (one input and one output at a time is enough)

pre-out if oDac is introduced

phono-preamp optional

Help is welcome and appreciated. Thanks for looking!

The solution to this would be either be an amplifier or a mixer which has a REC (record) out or similar. They are used to eg. save a live DJ set to a computer with full line level signal. The REC out would go to the headphone amp and the pre-amped, volume controlled "MASTER" signal would go to speakers etc.

I saw a Rotel stereo amp which had this at the local shop and tried a DJ-Tech 4-channel mixer but unfortunately the USB-portion of the mixer broke down so I had to send it back. Was also too big for desktop use.

Still looking for options :]