Onganju

If you are seriously doing any sort of striking, you should wear hand wraps. As stated above, you don't want to begin regretting the fact that you did not wear them.

Even with the MMA/Grappling gloves, it is a good idea to wear wraps. If you want to wear wraps under your Grappling gloves, buy yourself a Junior or Kids-sized hand wrap (like this). The wraps are shorter and thinner, so they don't add on the extra heft that won't fit into a smaller glove that standard wraps do. You'll end up not wrapping your thumb and using up less wrap around your wrist.

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