Hi Alice
I'm an Osteopath so de Quervain's disease is part of my normal work-load, although I have not seen many cases.
Reference to my books states that the problem is usually inflammation of the tendon sheaths of the Extensor Pollicis Brevis and Flexor Pollicis Longus muscles cross at the base of the thumb, in the soft bit of the wrist between the thumb and end of the radius bone.
The inflammation is usually caused not by a single injury but by repetetive actions, such as digging the garden with a spade or fork ~(common at this time of year), using a hammer, or more frequently poor posture while using a keyboard.
As you state that you would rather avoid hydrocortisone injections (I don't blame you) why not try ARNICA, a homoeopathic remedy in tablet form. Arnica is an anti-inflamatory and can be taken with any prescribed medication you may be taking. There is no interaction with prescription medicines. Arnica can usually be obtained from your local chemist or drugstore.
Application of ice-packs will also help, but be sure to wrap the pack in a cloth to pevent "freezer burn" on your wrist.
Also a splint can help, but it needs to be what is known as a "Cock-up" splint. It needs to hold the wrist in slight extension and abduction. In other words, the wrist needs to be bent slightly back and inwards, to slacken the skin and tissues at the base of thumb. Any form of soft or flexible splint will serve only to increase the profits of ther vendors: it will do you no good whatsoever.

Hope this is helpful. Please feel free to contact me either through the forum or by PM

Colyn.