but she isn't a supernatural character, she has from time to time fought them but thats not what her comic was all about. using Hydra as her background for her powers and training is good. i would have her looking for her father as the main story and keeping her on the move while being hunted by Hydra.
While I agree Spider-Woman herself wasn't supernatural, the tone of the comic was pretty similar to Angel. Her 50 issue comic run was full of supernatural characters and had a frequently supernatural feel about it. Morgan Le Fay, her arch enemy, was frequently trying to take control of her and claim her as her own. The comic even ended in a supernatural way with Morgan apparently defeating Jessica and seemingly killing her when she went to battle Le Fay in the astral plane with Magnus the magician (who was both there at the start and end of her comic).
Then there was the Brothers Grimm, Nekra, Waxman, Werewolf by Night, Hangman, The Shroud, Madame Doll, etc. And even if they weren't completely supernatural, the villains were rather creepy or macabre, such as Gypsy Moth, Daddy Longlegs, etc.
It was only from issue 20 onwards (after encountering Spider-Man) that she finally decided she was an actual heroine. Before that she was rather morally ambiguous and couldn't quite decide whose side she wanted to be on. Then she became a bounty hunter, and then a private investigator, first in LA and then later in San Francisco where, in the last few issues of her comic it came full circle and the supernatural tone was back. She continued as a PI after she was brought back to life by Dr Strange and the Avengers and had lost her powers. So the PI aspect is even similar to Angel.
The only time she really operated as an agent was actually before her comic, during the Marvel Spotlight/ Marvel Two-In-One years when she was sent to kill Nick Fury/ battled Ben Grimm, and was still an agent of Hydra who thought she had evolved from a spider. Jessica was still a rather creepy character in the beginning though.
It's only in recent years when she was given her powers back by Hydra prior to New Avengers that she began operating as a spy again. However, for most of New Avengers that was Veranke the Skrull Queen anyway.
For reasons stated above, that's why I think if she had a tv series or a movie, it should be on the CW or should be made to appeal to Twilight/ Buffy fans. It doesn't need to be radically retooled at all, because it is already in that vein. After all, Buffy herself wasn't supernatural but fought supernatural villains. Jessica Drew is much the same.
So I would say the template for Spider-Woman would be a cross between
Dark Angel, Buffy and Angel. Dark Angel had Jessica Alba as someone who had been groomed as a child by an evil organisation to be a killing machine but had then escaped. Buffy had SMG as a non supernatural but super powered female fighting mostly supernatural villains. And Angel had David Boreanaz as a vampire PI investigating macabre cases in a very dark LA. Incidentally, Spider-Woman's nickname in the comics was the Dark Angel of the Night.