I wouldn't recommend using a relaxer. The way it alters the chemical structure of the hair it can make it limp and lifeless which would leave you with the opposite problem from what you already have.

A better option might be to use a mild perming solution WITHOUT the neutralizer. After applying the perming solution and leaving it in for the allotted time you would rinse it out of the hair and comb it to get the hair in the position you want, then allow it to oxidize for at least 24 hours before washing it out. Skipping the neutralizer will help protect the hair from damage.

This might be tricky because you aren't using any rods to set the hair into place. On top of that the hair has already been through so much processing that another chemical process can leave it even more fragile than it already is, or even destroy it altogether.

Proceed with caution!