PSU are generally for reserves only. If you are going regular active duty, you will probably not be assigned to a PSU. If you are reserve, you should already know your unit, your assignment and most other pertinent information.
The swim portion of boot camp you can do whatever is most comfortable to you without it being doggie paddle or some other such kindergarten type swimming style. You can do breast stroke or side stroke. Just so long as you can do it and don't look like a drowning monkey, you'll be fine. I tried looking real quick on the USCG forum but I couldn't find it... there is an entire thread about swimming. When I find I'll update my post with a link. In the meantime you can check out the forum. There are a lot of good questions and answers there, asked by Coasties/potential Coasties and answered by Coasties. WWW.USCG.ORG forum
http://www.uscg.org/Forum/aft/6289.aspx#61547 link to a swimming question & answer
While I stand corrected that there are active duty personnel at a PSU, the likelihood of getting one is slim. I pulled this directly from uscg.mil site....
WHAT ARE PORT SECURITY UNITS?
Coast Guard Port Security Units are deployable units organized for sustained operations. They can deploy within 96 hours and establish operations within 24 hours. PSUs conduct OCONUS port security in support of requesting regional CINC's. They provide waterside protection to keyassetss (e.g. pier areas, high value vessels, harbor entrances) at the termination/origination point of the Sea Lines of Communications (SLOCs). PSU's may operate in U.S. territorial waters under the direction of a Coast Guard or Maritime Defense Zone (MDZ) command or in foreign waters as part of the Harbor Defense Command (HDC) within the Naval Coastal Warfare Command Structure.
Each PSU has 6 fast and maneuverable Transportable Port Security Boats (TPSBs) - 25' Boston Whalers outfitted with two 175 horsepower outboard engines. The PSU has a large suite of weapons. Each unit is outfitted with spare material, pick-up trucks and vans, boat trailers, transportable kitchens, tents, and DoD-compatible radios. They maintain an inventory of equipment and spare parts to sustain operations for up to 30 days. Ongoing logistics support provides routine replenishment. All personnel have required individual gear for field operations.
Each PSU is staffed by 140 reservists and 5 active duty personnel. Personnel prepare for contingency operations during weekend drills and normally participate in either an exercise or specialized training during two weeks of annual Active Duty.
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http://www.uscg.mil/lantarea/psu305/aboutus.asp There is the link. The chances of someone actually getting assigned there would be astronomical since there are only 5 active duty personnel.