Depends on my character.
I'm playing through Skyrim again (on PC and hence modded & DLC'd up the whatsit to be a brutal version - hypothermia, starvation/dehydration/exhaustion, combat upgraded to roughly Mount & Blade level lethality - if you don't block and take cover you die fast).
Character One: Malleus, Imperial, lvl 23, Dragonborn and Conqueror of Skyrim
A vicious hulking sadistic Imperial enforcer. Somewhere between Khal Drogo and Jaime Lannister in nature. Think of Sarevok with an 18+ rating rather than a comical bad guy vibe. He's the kind of guy who, upon butchering a Stormcloak camp, will shieldbash into submission the final shieldmaiden survivor because he likes his 'prizes' to be only subdued rather than comatose. So no, he usually doesn't take the peaceful option. Malleus is not someone you want to fight, slight, or even meet. An attack dog (bear?) wielded by the Empire as, essentially, a means of repression. A hammer by any other name.
Character Two: Faye, Breton, lvl 17
Faye is a delight to be around. Spends most of her time travelling to and from her home in Marthal on various magical excursions, an alchemist and summoner primarily. Handy with shock destruction magic, she relies upon her summoned creatures to protect her for the most part. In fact, she has never actually used so much as a dagger. Due to the harsh environments she travels in she must rely upon fur lined clothing rather than 'mage apparel' or armour. As she can't always summon protection in time she will try to avoid conflict as much as possible, and tries to help others as well however she can. In a realm of civil war and dragon attacks, she is a shining star of comparative goodliness. So, yes, she will always take the 'non-violent' option if she can (I actually wish there was more interaction possible with the Forsworn rather than just 'raaaar die!!!').
(as a side note, Malleus has something like 35,000 Septims just sitting about; and regularly tosses away items worth hundreds of gold; he regularly throws away more than Faye has ever held at once)