Danyforreal, hi, we'll get this working for you somehow!  You can be the first in the world to do this!  I'll show how to do it without soldering too if I can.

We'll try the direct connection between your 2 units first.  method first. I'm thinking the worst that can happen is the bose may get too high a signal at even the lowest volume of your dmm & distort the sound, but I very strongly doubt anything will be damaged (especially the bose!) if we get this part wrong.  With a small speaker your dmm has it would be lucky to be a watt going into it at max volume.  You may have to quickly dive for the volume control of the bose that's all!

Trouble is, a bit of wiring up of a little 'interface' circuit would then be needed to get the signal level right.   I've already found a suitable interface circuit if you need it.  I'll post that here for you as well.  Many thanks to Tomi Engdahl <then@delta.hut.fi> for that info!  Nevertheless, we could come up with a 'no solder' way of wiring that up for ya!  I found you a suitable 'no solder' jack to mount in your 'dmm' as well, so no soldering here either!

I've made up a 6 step method for you that I use myself to 'tap into wiring' without damaging the existing wiring, & it's a reliable, flexible, & long term connection!

You could use this method to modify your dmm without soldering. Calrad electronics in California make a nifty phone jack, for example, that you don't have to solder to! - it's got screw connections! Item number 30-491T  Looks like if you buy it through krp electronics you can get it for half the price!   You'll find it here =>

http://www.krp.com/PANEL-MOUNT-35mm-STEREO-JACK-W-TERMINAL-SCREWS_p_3078.html

Check the length of it's thread to see how thin a panel it needs to fit. Find a spot on the back or front of your music maker, & drill a suitable sized hole for the jack to pass through snugly. Then you just need to connect the black wire that goes to your internal speaker ALSO to the earth connection of your phone jack.

A very similar situation with the red wire to your internal speaker, except we need to join the other 2 terminals (L & R) of the jack together first, or you'll hear the sound in only one side of your nice soundlink speaker!. You mentioned only one speaker in the music maker, so I'm assuming that it's mono. I've made a pic for you of how it goes together.

Hopefully this setup won't be too touchy on the volume so you won't require any other mods, but we can do it if it's required.



___________________________________________________________________________________________
NO SOLDER WIRE JOINING METHOD - IN 6 STEPS  (follow pics called step 1 to step 6)

Step 1 => Carefully remove about 5mm of insulation from the wire you
                  are tapping into without damaging the strands of wire.  I first
                  carefully nip a mark all around the wire at each end where I'm
                  going to remove the insulation without cutting into the  wire
                  strands. The whole  idea is to NOT damage the existing
                  wiring.  A stanley knife or a  sharp pair of small wire cutters
                  should do the job if you're careful.  Take your time.

Step 2 =>Strip about 15mm of insulation from the end of the new wire
                 you are going to run to the new jack.  Line up the end of the
                 insulation of the 2 wires next to each other.

Step 3 =>Twist the strands of the new wire around & around the existing
                 bare wires' strands you exposed & along them, in a tight sort
                 of spiral using the 5mm to 'use up' all  15mm of loose
                 strands.  You can 'form' the wires so their wire ends are lying
                 all nice & flat & parallel with a little work.

Step 4 =>Stick about 20 mm of electrical tape centrally across the join,
                 so it evenly covers up the bare wires.

Step 5 => Tightly & neatly wrap the tape around the wire bundle, trying to
                  keep it from spiraling too much, but still tight.  Try not to spin
                  the wires themselves around while you do this - you are
                  wrapping the tape around the wire not the wire around the
                  tape!  Plus you risk fatiguing the connections between the
                  speaker & the pc board.

Step 6 => Wrap a small cable tie around the centre of the join & tighten
                  it up good & firm.  Cut off the excess cable tie end close to the
                  lock part & I can pretty much guarantee that connection for a
                  lifetime - unless it goes underwater!  It won't fatigue like a
                  soldered joint can when the connection is moved around.
_________________________________________________________



You can use an off-the-shelf stereo 3.5mm male to 3.5mm male audio cable to connect the 2 units together. No mods to your bose, & no mods to the cable. You just have to decide how long a cable you need between them. So yeah, electrically, it looks like a perfectly feasable idea. Be good to hear how you progress.  Good luck! 

I forgot to include the diagram for you!  Sorry bout that.  I've included it this time.  Also there's a pic of the type of cable you will need to connect the 2 units together.  Hope it helps.