Well, if you want to be overly cautious, that is of course your choice. I just told you what I now from experience: you can get a re-entry permit using I-131; the permit looks just like a passport and you can use it as such (the permit itself does nt say anything about the reason it was issued). There is nothing to preclude you from using the permit for short trips in addition to a long trip that you are planning, say for later on (and may change your mind about). I think it is reasonable to assume that no-one is going to bother you about the reason you got it. This is the case with Advanced Parole for I-485 applicants for example. Even though the instructions still say that you are supposed to give a reason for a particular trip with dates etc on an AP application, INS does not care about it now. When I was applying for an AP, I just wrote that I am eligible for it as an adjustment of status applicant and got AP with no problems. You could try a similar thing with re-entry permit: file an application and leave the reason for requesting it blank or write that you are eligible for it or even write that you are having trouble renewing your passport and need a travel document. In the worst case they'll reject your I-131, but this would not affect your GC status and you would have been perfectly honest...
On the other hand, unless you got I-485 approved
in a refugee/asylee category to start with, you cannot ask for a refugee travel document now that your GC has been approved and processed.