Please know I mean no disrepect to but I think his/her solution would, in effect, add additional artwork to Picasso’s painting, which in a certain sense would be disrespectful, and IMHO it would not give the impression you would be attempting to convey. Where you would be trying to give an even greater weight to the painting by having it mounted on some of the detritus of war, it is much more likely to appear to others to be amateurish and like you’re trying too hard. You see all sorts of things like this in local art shows and festivals. There is a big difference between making an artistic statement and *trying * to make an artistic statement, sort of like the difference between being funny and trying to be funny.
I would like to say again that I mean no disrespect at all to NoCoolUserName. He/she is trying to be helpful and come up with a good idea, and at first glance it does appear to be an excellent idea. But I’ve had enough experience around amateur art to have a pretty good idea how this would play out in real life.
Again, I too, would go with a simple black frame and let Picasso himself be the one who makes the statement.
And no offense taken. I’m not an artist, and I don’t even play one on TV. I play the guitar and I just help NoCoolSpouseName when extra hands are needed. I spoke my opinion, you spoke yours and we’re all pals here.
NoCoolUserName, thank you for taking the time to respond and for letting me know I was off the hook. I appreciate it. 
Mithril, you will let us know what you decide to do and how it turns out, right?
I have no clear idea of the size of the reproduction you are going to hang, but that might be irrelevant to the suggestion. I found the buff/mocha background on the site you linked to in the OP to have the right “feel” to it. If I were hanging it in my home, I would find a matte such as that, give it about a three-inch border, and surround it with a one-inch ebony frame.
StarvingArtist, I’ll even post a picture, if I can scrounge up a digital camera. You made a good point about not trying my own art project, but now I’m in the mood to do it. If I try it out and it doesn’t work (likely), I can always frame it in something more standard. I think I’ll go with a thin black frame with an off-white (bone, ecru, antique linen…) and blue-gray double mat. Of course, I would have to look at it at a frame shop first, but it seems like that would be subtle enough to not distract from the print.
Thanks, everybody, for your ideas. I just have no grasp of what colors work well together, which was particularly tough when I used to sell paint and people would ask me for my opinion!