Like the Templars, the Hospitallers would have borne the same arms on their shield as on their banner. David Nicolle has also assumed this, in his Osprey book on the Knights Hospitaller, 1306-1565. The earliest pictures of Hospitaller shields that I have found are from Caoursin's account of the siege of Rhodes in 1480 -- these do show a red field with a white cross. This is not absolutely conclusive, but it does seem most likely that the Hospitallers' shield had not changed, and had always been red with a white cross.
Alas, I do not know of any Hospitaller frescoes like those at S. Bevignate in Perugia. Matthew Paris's _Historia Anglorum_ has one image of the Hospitallers' banner thrown down in defeat in 1239: this shows a red field with a white cross (London: British Library, MS Royal 14 C vii, fol. 130v). Again, in one manuscript of his _Chronica Majora_, Matthew showed the banners of the Hospitallers, the Templars and the king of France: and again the Hospitallers' banner has a red field with a red cross (Cambridge: Corpus Christi College, Parker Library, MS 16 fol. 141). He never shows the Hospitallers' shields. I think that it would be most likely, however, that the Hospitallers' shields matched their banner.