The installation instructions don't mention screws at all but with all sorts of easy to use exterior screws available today it seems one would be less likely to damage the frame of the window than hammering in nails. It may be that the nails allow for more expansion. Also are the shims absolutely necessary? Thanks
plastic windows are extremely temporary. i know i know there's some sort of long warranty but for real, they don't last very long THEY'RE MADE OUT OF PLASTIC!!! install em how ever you want. if you were building a house out of legos (i'm sure pulte or someone's already workin on that) then you could just snap em in. bad buy, too late, good luck! or should i say good luck to the next guy who buys your house that gets to replace the windows again.
is the window new construction or repplacement? if new , it has a perimeter flange around it and nails work best because of the size of the head and will allow the siding to lie flat once installed, old construction yes you need pan type head screws, coated preferred. shimms are recommended , but leave a little room for expansion and contraction as they are vinyl
If the screws have a large flat head, seems they'd be okay. Just remember leave them just snug the wood around the window needs to move