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Manta rays and sharks SWIM. 飛翔する means to fly or fly high, so this verb is not normally used for fish or ocean animals. However, in a poetic sense, you could use any verb you wish to express your perception; when you are diving, you see how they swim in the water below you, above you, etc. I believe that the big fins of manta rays and sharks could remind you of bird wings or else the wings of fighter jets and jumbo jets!
Thus, my second suggestion is to use the word fly with quotation marks: "fly" across the water.
Ref. goo dictionary
mkj United States Local time: 10:08 PRO pts in pair: 159
2 days11 hrs confidence:
Explanation: If you ever dive along a reef, you will see fish, jellyfish, and turtles swim by. Swimming yourself, you may feel at one with them. The feeling is entirely different when the mantas and sharks arrive. Unlike you, the other swimming creatures, and the corals, they do not appear to be affected by the current. As the sentence provided says, they fly (at times soaring, gliding, or hovering)within the ocean with complete composure. The experience of encountering them tells you right away that the ocean is their world and you are an intruder. It is awe-inspiring in a way that "serenely swimming" is not.