Power ratings on speakers are often way out to lunch. For the vast majority of times, the speakers are rated for a maximum power output, but even then...
I've seen people blow "300W" speakers with a 12W factory deck. (And good speakers at that, not crap ones. I've also powered factory "20W" speakers with an 80W amp for years.
Speakers are far more sensitive to distortion and clipping than they are to raw power. Power handling is all about heat dissipation, and when there is distortion and clipping, no matter what, there will be a lot of extra heat, which will cause damage to your voice coils.
What's far more important is the sensitivity rating of the speakers. Look for the rating of how many dBA you get for 1W at 1 meter. Something between 85-90dB at 1W/1m is pretty typical, for good aftermarket speakers with a median being around 88. this is going to tell you how much sound you will get for what power output. (Factory speakers are often at the lower end of this range, so often "high power" speakers will be louder, even at the same power level. Go figure.)
dB levels are logarithmic, so if your speakers are 88dB/1W/1m, 2W will generate 91dB, 4W 94dB, 8W 97dB, 16W 100dB, 32W 103dB... And so forth.
In general, I think that upgrading the speakers is probably just a good idea, and should work fine with your factory deck if you keep the volume control under ... control.
