As shown and given your comments in text and comments, connecting the two braids makes sense and will PROBABLY be OK.
Q: How hard can this be?
A: More than it appears :-).
If both braids connect to their local negative wires I'd do it without question BUT be aware that you could just possibly get a signal earth loop (two earth wires, one via braids and other via negative wires form a pickup loop. This MAY cause hum in audio systems but usually no problems in digital systems. If braids and negative wires are not electrically connected at both ends I may leave the braids disconnected - it has a 99%++ chance of working OK.
The two systems are at the same ground potential as shown by using the common USB negative rail. It is very common practice for system metalwork to be at ground negative potential BUT not always.
In most cases where this is not the case then the cases / metalwork may be at mains ground potential if a mains power supply is used but not at output negative side potential, which may be floating relative to mains ground. In most cases connecting output negative to mains ground will do no harm.
NOT connecting the shields will usually do no harm in most cases. If they are connected to their local negative supply then it makes no difference. If they are not connected electrically to anything (which is unlikely) then it makes no difference. If they are connected to their local mains ground AND you run the two devices from two power points that have a ground potential difference (which difference you really should not have happening ! :-( ) then you could get a shock by touching both systems grounds at once and faulty operation may occur. If both system power supplies are connected to the same mains outlet then the above is not liable to be an issue except under certain mains fault conditions of one power supply - and this is liable to be very very very rare.