There is some parallel and precedent regarding the discovery of the Tutor war ship Mary Rose, which sank in the solent in 1545 as Henry VIII looked in horror. The Mary Rose was salvaged in 1982 and is now on display in Portsmith. The remains of the ship's company were buried in the Anglican cathedral in that city. But there are differences with the case if Richard. The Mary Rose was lost during the height of the Reformation and it would be impossible to determine religious sentiments of the men during this period of transition. The burial service itself was joint Catholic and Anglican and used a burial service from the period. That seems appropriate, as the crew was likely something of a hybrid, neither Catholic nor fully Protestant.
But Richard was a Catholic.