The OCS accessions for EOD and NSW are incredibly slim. If you aren't already working with those communities, the likelihood that you will be able to get in are slim to none. When I redesignated at OCS, I put EOD as one of my choices. I ended up only being offered SWO since I didn't want to be a Nuke.
I found out a week later that there were only 2 EOD OCS slots for YG12 and both of them showed up to the class mine were the Candios for. They were/are good dudes and both were prior-enlisted EOD bubbas coming from the Fleet. The EOD community is incredibly small so it's hard to get into. You would likely have better luck becoming a SWO and then hunting down the EOD command on base and trying to lateral transfer into that community. Same with NSW, except they are even pickier and require that you go through a bunch of interviews so they can gauge your personality and make sure you'll be a good fit.
All that said, if you want to try to get an EOD or NSW slot, put it down on your list and see what happens. You'll at least be given a dive physical and may luck out. You miss 100% of the shots you don't take.
Forgot to add: If you become a SWO and then lat transfer into EOD, you will get to wear one of the coolest warfare pins in the Navy, the Navy Special Operations Officer Pin.
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