I deleted it due to needless detail and speculation and lack of proper sources on some paragraphs. I guess though that the following considerations are harmless and of general interest (not Rossi-specific).
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a-b) If you're assuming that a BLP-like reaction occurs, initially mostly light, EUV and soft x-rays (as often mentioned by Randell Mills, e.g. here - a randomly picked paper from his published works) as the hydrogen atoms transition towards lower energy levels. These would have an energy of a few keV at most depending on the level into which they fall. Some people like Simon Brink have calculated the energy released by the transition of hydrogen from the ground state to the various sub-ground levels (for example see table halfway in this page).
c) Any sufficiently thick (fractions of mm) transparent material would attenuate all of the x-rays produced by this step. Since they would have quite a low energy the difficult part would actually be detecting them under normal conditions. Check out attenuation distances with the tool available on http://henke.lbl.gov/optical_constants/atten2.html.
d) It can be supposed that if the shrunken H atoms could be disposed of or somehow excited back to the ground level before they can accumulate and get triggered for a larger energy release, perhaps spontaneous nuclear reactions and other emissions caused by their short atom-atom distance/small size could be prevented. However for this to produce useful energy, the transition to lower levels must yield more energy than that required to go back to higher levels, but seen it this way this could be considered as getting energy from "nothing" and be unphysical.
The only material I'm aware of that would be translucent to soft x-rays would beryllium or beryllium oxide.
To cynics the idea of shrinking hydrogen to release energy and then allowing it to grow to the ground state again would be unphysical. However, if we are willing to accept the idea of a sea of vacuum energy then it becomes possible.
I'm thinking that it's possible the conditions that allow extraction of vacuum energy and the conditions that allow LENR could be extremely similar. What would be very interesting is to run the same experiment with different combinations of gases (with or without gases that are expected to participate in LENR) and see if any excess energy appears. I'd find it fascinating to test the optimum noble gas combination alone and then test the same combination with hydrogen and then with hydrogen and lithium.