While I applaud the wizard's chutzpah...

The Accidental Activation Rule Is Terrible

I fully agree with KRyan and Ernir that ignoring the accidental activation text is the best way to go. It causes more problems than it solves. I'm of the opinion that it's included only so the DM can have hilarious situations occur at the tavern because the wizard forgot the command word for his wand of fireballs was hubba hubba.

But If You Must Use It...

If you're dead-set against totally house-ruling it away, here's one way to run it.

The command word text reads, in part,

A command word can be a real word, but when this is the case, the holder of the item runs the risk of activating the item accidentally by speaking the word in normal conversation. More often, the command word is some nonsensical word, or a word or phrase from an ancient language. Activating a command word magic item is a standard action and does not provoke attacks of opportunity.

Emphasis mine. Not possessor, by the way. The holder specifically--as in what one does with a hand.

The description of the pearl of power reads, in part,

This seemingly normal pearl of average size and luster is a potent aid to all spellcasters who prepare spells (clerics, druids, rangers, paladins, and wizards). Once per day on command, a pearl of power enables the possessor to recall any one spell that she had prepared and then cast that day. The spell is then prepared again, just as if it had not been cast. The spell must be of a particular level, depending on the pearl. Different pearls exist for recalling one spell per day of each level from 1st through 9th and for the recall of two spells per day (each of a different level, 6th or lower).

The wizard can create multiple pearls of power all with the same command word. The wizard can activate one pearl of power in the wizard's possession as a standard action using that command word. If the wizard holds in her hands two or more pearls of power when the command word is spoken as a standard action to activate a magic item, one of the pearls of power in wizard's hands activates, determined at random.

(This assumes that the DM determines that a held magic item takes precedence over a merely possessed one with the same command word and that the DM wants to stick to the (actually far more important) rule that activating a command word magic item takes a standard action, and therefore simultaneous magic item activation can't happen accidentally, much less, like here, as some kind of faux accident. I went with random determination as that makes sense if multiple pearls with the same command word are deliberately held and the holder fails to specify which one to activate when the command word is spoken.)

Only [...] the various prerequisites required of the new ability to be added to the magic item restrict the type of additional powers one can place.

You are not creating a vorpal sword; the vorpal property is already on the sword. The relevant rule, quoted above, indicates that only the prerequisites of the new ability are relevant in this case. Thus you do not need to meet the prerequisites of the existing properties; you aren’t creating those, and the closest thing to saying you need them says:

Note that all items have prerequisites in their descriptions. These prerequisites must be met for the item to be created.

You aren’t creating a vorpal sword, so you don’t have to meet the prerequisites of vorpal. You are creating a new flaming property that happens to be placed on an already-vorpal sword.