Without Richard, how does the Crusade go? If all Christian outposts in Outremer are taken, logistics could kill Richard's plans. I think the French and Germans could free Acre at the least, providing a base to operate from and easy landing of supplies.
Without Richard's support, Guy de Lusignan loses the kingship of Jerusalem to Conrad de Montferrat, unifying the Kingdom of Jerusalem instead of the civil war that existed between the two. That alone could make a big difference. And it has been suggested that the assasins that killed Conrad were hired by Richard. If that is so, he may not have reason to do so in this TL. If Conrad lived longer, he may have founded a strong dynasty. Whether this would make any difference in the long run is open to debate. It could give a few decades or possibly(doubtfully?) centuries to the life of the Kingdom of Jerusalem.