Claria is dye-based for the colours and pigment-based for black. I don't know what you mean by "regular" ink, but if the cyan and yellow inks you are using are also dye-based, then yes, you should be fine mixing Claria with them. If the other ink you are using are pigment-based, then you may get some odd effects, especially with glossy photos.
So, my XP-970 I using Claria inks where is only one Black cartridge and that means this black is a pigment? I'm asking because I want to install a ciss and I'm not sure what inks I need. I think color inks T6732-T6736 should be ok. I'm not sure about black T6731 or 105?