For the past three years in my gaming, I have had no division between divine magic and arcane magic, and I did it for some of the same reasons you did, such as to make the truth about magic and divinity less clear cut. I don't have things like gods walking the earth, and I kinda got tired of having to put undead in every few adventures to give the cleric something to turn.
Anyway, I handled the change pretty easily. This is my insight after several years of tweaking:
* Keep all the existing classes, just remove the part of the text that explains how they get the magic. That's up to the GM and player to decide. If someone wants to play a cleric, they can use the rules for the cleric, since those rules are fairly balanced. They keep clerical spellcasting restrictions.
* For the wizard and sorcerer, every spell is available on the spell list. However, I've noticed that very few folks have chosen healing spells, because of my next change.
* To reduce the reliance on healing spells, I use a system roughly similar to the Wound Point system in Star Wars. Characters all have a number of Wound Points (WP) equal to their Constitution (3/4 Con for small races). You only take WP damage if you run out of HP entirely, and WP heals at a rate of 1 per day. HP, on the other hand, heals at a rate of 1 per level per hour, like subdual damage. Thus, in this system, HP represents all those close shaves and minor flesh wounds that heroes can endure, while WP represents really nasty injuries that only happen once you're too worn out to dodge anymore. You can heal those close shaves pretty easily, so you usually don't need healing spells.
Healing spells cure their normal amount of HP, plus 1 WP for every die of healing. So Cure Light Wounds would heal d8 HP and 1 WP. While you have wound point damage you suffer a -2 penalty to all rolls and checks.
So that's the rules-end of the bargain. The story-based aspects of the game are of course unique to my own world, but I find that I have a lot more leeway on character and culture design. Plus, I'm working on making a perfect "Single Spellcasting Class" system in the revised edition of The Elements of Magic.