You live in a BEAUTIFUL area I wish I could cruise there myself.
But seriously, guys do what you are talking about in ocean kayaks so I doubt a good dinghy will be less able to deal with currents. You can always wait until the tides change anyway.
If you're gonna do this, esp in cold water, DRESS FOR IMMERSION. Wear a drysuit or at least a wetsuit for if you capsize.
As far as choice of trailerable affordable dinghy, Smack has a thread about a beach cat he picked up for $200 and will be in sailing shape for a total of $600 (I think). Beach cats are extremely seaworthy, and are fast enough in a breeze to outrun a modest current without too much trouble. Super stable too, so the likelyhood of capsize, as long as you are prudent, is pretty low and there is plenty of deck space for gear. They are hard to paddle when the breeze dies however, whereas a dinghy can simply be rowed. A motor on a sailing dinghy seems unwise though, since it will capsize at some point and your motor will be damaged. Also, motors are expensive you are better off investing in a screacher or something similar for light winds IMHO, if you are on a serious budget. I've even made a jib out of white duct tape and white pvc tarp material that worked well enough for a full season, alot of guys do this for small boats and dinghies.
forum.woodenboat.com has a ton of people who do this sort of thing, that might be a good place to do some searches. search the term "sail and oar cruiser" or "beach cruising" or something. This is a cool open boat cruising site also: www.openboat.co.nz
One more thing, if you have a place to store the trailer there are some very small keelboats that may still be picked up for almost nothing used, they may require some work though. I'm thinking like a Rhodes 19 or something. But no dragging that
up a beach...