Yes, you can make it work but it will take "some work".
In mid 1994 they changed a couple of minor things on the model which is (essentially) mechanically identical from 1988 until about 2012 when they stopped building the model all together (think they ceased US sales in about 2005 because of EPA regs, but sold as export only until 2012).
Anyhow, in mid 1994 they changed something that will effect the swap between those two model years. They slightly modified the exhaust plate/tube, in particular the (mount) for the water tube and the water tube itself.
On your 88 model the water tube will be attached to the exhaust plate by a little (clip) with a couple of screws - screws right into the bottom of the plate (at the front of the motor). The top of the water tube is flared (which is how it stays in that clip - can't recall the name of that "clip" in the parts list) and then the rest of the tube is straight all the way down to the lower unit. It passes through a hole about mid way down the casting in the (leg) exhaust housing.
(hope I don't lose you here)
On the post 94 models they got rid of the clip and the flare at the top of the tube and it, instead, is simply "stuck" into the exhaust plate with a grommet. To stop it from pulling out when you remove the lower unit, they put a flare in the tube itself part way down that prevents it from going through the hole in the casting on the exhaust housing.
The problem is, the moved the location of that "hole" in the exhaust housing so a new water tube won't fit properly in the old housing. To get around that you can take a long drill bit (like a cable installer uses) and drill out that hole big enough to allow that flare in the tube to pass. This does create the possible issue of the tube pulling out when you remove the lower unit, but when assembled there is no issue.
Now, because the upper end of the tube is "different" you also have to swap exhaust plates along with the leg, and the lower unit to get the different water tube to connect. That requires pulling both powerheads, removing the exhaust plate and changing it on the unit you want to use, replacing the exhaust gasket and the powerhead base gasket and putting it all back together.
If you have both complete motors and the powerhead on the 15 short is the bad one I would simply pull that and put the powerhead from the 15 long (the good one) in it's place - only need replace the base gasket and button it all back up - that is a whole lot less work.