What is a safe and accurate technique for shuffling cards?
When I shuffle I use a mixture of two techniques: riffle and stripping (as defined quite adequately in the Wikipedia article on shuffling). Riffle separates adjacent cards while stripping cycles cards from the top of the deck to the bottom.

I use both because riffle alone will very slowly push cards in the bottom half of each cut down, but tends to leave the top of the deck the same; stripping mitigates this drawback. Stripping alone takes too long to separate adjacent cards.

Early in the game when the deck is small (&lt; 20 cards) it's very difficult--and unnecessary--to riffle so I only strip. 

Wikipedia points out that riffling can be hard on cards; however, I've found that damage typically occurs because the person isn't good at shuffling and either excessively bends the cards or doesn't get good interspersion between the cuts. Being able to execute a bridge also reduces card wear as it evens out the bending and prevents the cards from acquiring a camber. In fact, I think proper riffle shuffling breaks in cards and makes them less stiff and prone to sticking to each other.

It seems that you're looking for something potentially easier to learn the riffling, but nothing is as fast (vital in Dominion) or as reliable at randomizing a deck. Honestly, anyone with reasonable motor skills should be able to learn to riffle with practice.

Wash shuffles are great for randomization but totally infeasible for Dominion since they take so long and take so much table space.

Weaves have the same end results at riffles, so if you weave you should strip as well. A weave is easier for many people to do, but will damage cards quickly as you have to slam or wiggle the edges of the deck together. Cards were made to return to their original shape when gently bent; they were not made to take stresses on their edges.