The box enclosure type will not affect whether or not you can use any particular tweeter. Speaker enclosures are only needed for subwoofers, woofers, and some midranges. Pretty much all tweeters are fully sealed devices, so their "box volume" is contained within the tweeter itself. When building a speaker, you have to carefully design the box to suit the woofer, but to put a tweeter in the box, all you have to do is mount it in the box.
However, figuring out which tweeter is *optimal* for your application is whole other story. The main thing you need to figure out is if this tweeter will work with the existing crossover in the speaker box. First, you need to make sure the replacement tweeter can handle the crossover point of the crossover in the speaker box. Generally, small-diameter tweeters require a higher crossover point, and larger tweeters can handle lower crossover points. This particular tweeter can handle fairly low crossover points (2.5kHz with a 12db/octave filter slope works well), so you should be fine in this regard. Next, you need to make sure the replacement tweeter has the same impedance as the old one, to ensure that the same crossover point is achieved using this crossover. If it isn't then you'll either need to use a different tweeter with the right impedance, use a whole new crossover, or adjust the new tweeter's impedance by putting a resistor in series with it (but note, this will lower its sensitivity). Finally, you may need to add an L-pad or modify the existing L-pad in the crossover (if it has one) in order to adjust for the sensitivity of the new tweeter. If the new tweeter is more sensitive than the old one, and you don't modify/add an L-pad then there will be too much treble. Conversely, you could end up with too little treble if the new tweeter is less sensitive than the old one.