Swap is not a filesystem.
I don't think OSes take any particular care of how they arrange the swap space. Most filesystems either don't care or are optimized for rotating disk drives in that they try to privilege sequential reads and writes (i.e. avoid fragmenting files too much), which is not relevant on SSD.
Modern SSD drives (as opposed to cheap flash media) do their own wear leveling in firmware, so the OS shouldn't need to care about this. When the OS is writing to the same address, the firmware maps each access to different physical blocks, in order to avoid having many erase cycles to the same block. With an SSD drive in a PC or server, as opposed to a flash memory in an embedded device, flash wear-out is usually not something you need to care much about.
You may however want to reduce swappiness on SSD compared to HDD. Swappiness is a compromise: it's the parameter that controls whether the kernel prefers to keep file contents or process data in RAM. Higher swappiness means that the kernel is more likely to swap out process data in order to make room for file contents. With many workloads (but not always), a lot of file contents is only ever read, whereas application data is written relatively often, so increasing swappiness increases the proportion of I/O in the write direction. Since SSD are usually relatively slow to write, compared with reading, the optimal swappiness tends to be lower for SSD.