I don't think you should have a problem in swimming. In fact, you should have started swimming earlier and this would have decreased your stiffness problem because the buoyancy of water minimizes stress and relaxes the muscles to exercise better. I suggest you follow a few guidelines in the beginning.
(1) Find a swimming pool that has lifeguards seated at vantage points along the length of the pool.
(2) If you get cramps, do not panic. Float on your back. Let the affected limb relax. Use your other limbs to propel yourself to the edge of the pool.
(3) Try and do some warm up exercises for 5-10 minutes.
(a) Knee lifting.
(b) Walking at one point.
(c) Walking on tiptoe.
(d) Arm swings.
(e) Twisting in one place.