I would say that proper way would be to create editor descriptor that is providing possible values from your enum. For instance like this:

    public class EnumEditorDescriptor<TEnum> : EditorDescriptor where TEnum : struct, IComparable, IConvertible, IFormattable
    {
        public override void ModifyMetadata(ExtendedMetadata metadata, IEnumerable<Attribute> attributes)
        {
            SelectionFactoryType = typeof(EnumSelectionFactory<TEnum>);
            ClientEditingClass = "epi-cms/contentediting/editors/SelectionEditor";
            base.ModifyMetadata(metadata, attributes);
        }
    }

    public class EnumSelectionFactory<TEnum> : ISelectionFactory
    {
        public IEnumerable<ISelectItem> GetSelections(ExtendedMetadata metadata)
        {
            var values = Enum.GetValues(typeof(TEnum));
            return (from object value in values
                select new SelectItem
                       {
                               Text = EnumExtensions.GetLocalizedEnumValue(value),
                               Value = value
                       });
        }
    }

Then you need to decorate your page/block type property to provide necessary info for EPiServer to render dropdown for that property:

        [Display(GroupName = SystemTabNames.Content, Order = 7)]
        [BackingType(typeof(PropertyNumber))]
        [EditorDescriptor(EditorDescriptorType = typeof(EnumEditorDescriptor<HeaderType>))]
        public virtual HeaderType HeaderLevel { get; set; }

Then it's up to you how you implement `EnumExtensions.GetLocalizedEnumValue(value)`. There are many ways to implement custom localization provider (few samples here).

Simplest solution is to have a Xml file with resources and use something like this to provide editor for editors :)

Implementation to read localized value from Xml files via EPiServer infrastructure:

    public static class EnumExtensions
    {
        public static string GetLocalizedEnumValue(this Enum value, CultureInfo culture = null)
        {
            return GetLocalizedEnumValue((object) value, culture);
        }

        public static string GetLocalizedEnumValue(object value, CultureInfo culture = null)
        {
            culture = culture ?? CultureInfo.CurrentUICulture;

            Type type = value.GetType();

            string staticName = Enum.GetName(type, value);

            if (staticName != null)
            {
                string localizationPath = string.Format(
                    "/property/enum/{0}/{1}",
                    type.Name.GenerateSlug(),
                    staticName.GenerateSlug());

                return LocalizationService.Current.GetStringByCulture(localizationPath, FallbackBehaviors.Echo, culture);
            }

            return null;
        }
    }