I vaguely remember some rules on mixed close combat weapons (sadly I can't give a page reference). The example was a model armed with a Power weapon and a Power Fist. If the user chooses to strike with the power weapon, he gains +1 attack from the Power Fist as it's a close combat weapon and power weapons make no such exception to this rule. If however he strikes with the power fist, he gains the double strength bonus, but not +1 Attack, as the rules for power fists state that you can only gain +1 attack from another power fist.
To answer your question, you could strike using the pistol (counting it as a close combat weapon) and gain +1 attack, but you would do so with none of the Power Klaw's perks.
I know the wording of "A normal and a special weapon" sounds like it specifically countermands this, but that could be the wording taken too literally, considering this little shoutbox seemed to specifically address that issue.
To answer your question, you could strike using the pistol (counting it as a close combat weapon) and gain +1 attack, but you would do so with none of the Power Klaw's perks.
I know the wording of "A normal and a special weapon" sounds like it specifically countermands this, but that could be the wording taken too literally, considering this little shoutbox seemed to specifically address that issue.