I'm currently roleplaying non-caster character, who strictly avoids casting any spells. That means I cannot charge any soul gems by myself. Are there any NPCs that can charge my magic items for me?
I am using the following method for capturing souls, which does not require casting any spells. Thus, I can suggest this as another option.
1- Buy a weapon with "soul steal" enchantment. (The hunters in Winterrun sell one)
2- Disenchant to learn the "soul steal" enchantment.
3- Enchant a weapon of your choice with "soul steal" enchantment. (I use a bow for this.)
4- Whenever you kill a creature with this new weapon, you can capture its soul provided you have a gem available. You can then use the gem to recharge your weapons.
No. Although there were rechargers in Oblivion, there are none in Skyrim.
In addition to using a weapon enchanted with soul trap (bought or made), you can also take advantage of a perk that automatically recharges your weapons.
Death blows to creatures, but not people, trap 5% of the victim's soul, recharging the weapon
Of course, this requires that you level Enchanting up to 40, which you might not want to do if you're not a caster. You could always pay for training, rather than actually enchanting things.