^ Could be done one thing at a time, get the bulk of the work done then when finished, decide whether to swap in new speakers.
Whether the stock speakers can take the wattage depends on how high you crank the volume. With the stock stereo if it's cranked up, you'll get distortion that eventually damages the speakers. With a higher wattage amp, given enough volume, sure you could blow them, at a lower volume than aftermarket speakers rated for higher wattage, but you could blow aftermarket speakers too.
Above I mean if they aren't bypassed with a high pass filter. They can handle low frequencies too, but obviously that's more power getting to them and further limits the total volume the system can produce. Certainly you can do a high pass to them and continue using them... and if you do crank the volume up too high and damage them, it's a bit of the same difference in that you then replace them.
Clearly replacement speakers of decent quality would sound better, or of equal quality but new instead of ~ 25 years old, but I wouldn't pay a lot for fancy tweeters in the front door speakers because the speaker is so low that most of the treble is lost.
If you're insistent on good treble then you'd be better off with satellite tweeters but I don't know if there is room in the windshield pillars without them sticking out more than you're like (depending on the tweeter design, thin piezo type sound terrible and thin neo magnet type are more expensive), and if you add the tweeters you'll have to fiddle with balance since they'll be so much nearer your head (add a series resistor after experimentation to find the right ohm value). Then again there's ceiling mounted or dash or wherever you'd like to put them.
Given enough motivation you might even be able to cut holes in the top dash surface and drop in a dome tweeter for better wide field radiation. Since it's a tweeter it's not like the mount has to be very robust, just enough that it doesn't rattle from vehicle vibration.
