First of all good luck to your DS for the up-coming test.
Secondly, there are probably as many thoughts, opinions, approaches and plans of attack, as there are children. My thoughts on it are based upon my experience with two completely different learning types as far as children are concerned ie the self-motivator who loves work and the self-motivator who needs a gentle prod
I'd say that only you
know your son. What you have to be careful of, is that he doesn't dip, confidence-wise, so close to the real thing. Is he wanting to do it for himself and even if it is, is it out of a sense of panic, ie I'm not confident in my abilities or out of a sense of let's keep up the momentum cos I love it? Either way, I 'd probably chose which paper he does, with some care ie have a look and assess whether it's a little too challenging and therefore a risk, as far as his results are concerned. You could always let him sit it and then neither you, nor he look at it, in terms of marks, or results. If you have some 10 minute tests, then perhaps he could do those, rather than a full 50 minute paper (if that's what your son sits on the day)
My DD asked me if she could do tests the day before and I only let her do 10 minute tests. I trusted that she was asking because she wanted to and not out of a sense of panic. She said it actually helped her to still do them that close to the test itself, calming the nerves. We didn't do anything after she came home from school that day - we wanted her to have a rest, mentally and emotionally - not that it was possible, in reality but we tried.
I've asked if, with the benefit of hindsight, she felt it was the right move to do this and she's said yes.
All I'd say is, play it by ear. Life's a gamble, isn't it and the 11+ is full of dilemmas?