Possible to hide block header?

When using a block as a property for a page or another block. Is it possible to hide the header so that the block appears like a just a list of properties?

At the moment I have a blocktype called PagePuffBlock. This blocks has a local block of type ListingBlock. The remaning properties of this block are more like additions to the properties in the ListingBlock so when the customer wants to create a block and sees the heading "Listing" they get confused. 

This is the blocktype

    [ContentType(
        DisplayName = "Sidpuff",
        GUID = "136bac1c-ccea-4a89-be1e-ef9ee6ab7160",
        Description = "",
        GroupName = Global.BlockTypeGroupName.Puff)]
    public class PagePuffBlock : BlockData
    {
        [Display(
            Name = "Sida",
            Description = "Sida att hämta data ifrån ifall de andra listegenskaper inte är satta",
            GroupName = SystemTabNames.Content,
            Order = 1)]
        public virtual PageReference Page { get; set; }
        [Display(
            Name = "Länk",
            Description = "Länk för besökaren om inte sidans länk är tillräcklig",
            GroupName = SystemTabNames.Content,
            Order = 2)]
        public virtual Url Link { get; set; }
        [Display(
            Name = "Listning",
            Description = "Egenskaper som skriver över det som annars hämtas från egenskapen \"Sida\"",
            GroupName = SystemTabNames.Content,
            Order = 3)]
        public virtual ListingBlock Listing { get; set; }
    }

Is this something that's possible or am I working in a way I shouldn't be working? If so, please tell me.