I wrote this earlier reply about converted Iberian Muslims (or moriscos) emigrating to the Americas, hopefully interesting for you. In it I'm drawing mostly from Katherine Cook's work, afaik still the only monograph on the topic. She analysed a large number of judicial/inquisition documents that show that there were many cases of moriscos crossing over to Spanish America illicitly - similar to Jewish conversos.

At least for Spanish America I haven't come across Arab slaves. I assume that those would have been few if any cases because in Spanish America a) native Americans were enslaved in large numbers until the mid-16 c. and in smaller numbers until the early 17th c. And esp. b) Africans - many of them Muslims - were forcibly brought over in increasingly huge numbers also from the mid-16th c., partly to find cheap labor due to the native demographic crisis. So there would not have been much incentive to find other slaves - esp. with Spain and the Berber states and Ottoman empire not fighting any major wars since the late 16th c. (after the battle of Lepanto).