It's completely doable, and cost notwithstanding, it's very easy on 1983 and later cars.  All the parts bolt right in - the only thing you'll need to do is a little wiring, as the later headlamps and cornering lights use different connectors than the earlier ones.  In the front, you'll need the bumper (complete with lower air dam), the two cornering light clusters, the two headlamps, the grille, and the two bumper extensions (the plastic bits that go between the front wheel wells and the bumper).  In the back, you'll need only the rear bumper and its two extensions.  Your best bet is to either obtain a parts car or get in touch with a dismantler who can package all the parts - trying to buy the stuff piece by piece could be quite difficult, since there are little bits of hardware you'll need that may not be initially obvious.

After doing this, the only remaining visual cue that your car isn't one of the later ones would be the absence of side-markers - those little turn signals on the front fender.  If you're truly ambitious, you can cut the holes in the fender and splice wiring into the turn signal circuit.  The only exception to this would be MY1986 900s - the only year of the early-style bumpers to get side markers.

Do note the following:  900 Turbos have an oil cooler which needs direct airflow in order to function.  On 8v non-intercooled cars, the oil cooler is located just forward of the air box, between the radiator and the inner fender wall.  On 16v cars and all intercooled cars, the oil cooler is located underneath the lower cross-member - almost directly under the intercooler.  Each of these cars has a specific lower air dam designed to direct air towards these coolers.  If you replace the bumpers on an 8v Turbo without also replacing the oil cooler with one from a 16v, you may very well end up cooking your engine or turbo as airflow to the cooler will be almost completely cut off.  Relocating the oil cooler is not particularly difficult, but on earlier cars may require some drilling to mount the cooler itself.

Secondly, on some 1983 and all earlier cars, you will  encounter some problems mounting the aforementioned bumper extensions.  While the holes for their mounts should exist on all 1984 and later cars, they may not be there on all 1983 or earlier cars.  Drilling may be required - and that isn't fun.  Before getting into the conversion, check to see if they exist on your car.  The easiest way to check is by removing the windshield washer bottle from the right fender and checking for the holes along the front fender.