Nope, when anyone transform into rider, he/she can do martial art in limited extend. This is fictional and everything can happen, Rider suit give anyone magical power and fighting prowess they never have. Especially Heisei Rider consist mostly young person which have peaceful life suddenly have to fight against monster. Even at first they fighting poorly, after they get the suit, they will and have to show some martial art that they shouldn't have. Atleast Tsukuyomi have guts to fight monster in frontline even though most of it is fight to retreat. Not just shooting, she did kick tackling a monster before. Think of it as Rider power give her the strength to move and do anything she can't do before. Fighting style? Even if you have it but your body is weak to make it useful and you have a gun at your disposal, you will choose ranged battle especially if you against monster which can easily subdue martial artist. Now what if you have anything you need to make your martial art to be useful, like from a belt and a watch?