Yes you can. Problems you won't have...unless you are swapping between an MTX and ATX and haven't given thought to the components you need to swap: oil pan, tensioners, etc.
But if you just want to put an 89 engine into and MTX 93 then you will have no problems. A straight swap with no changes necessary whatsoever. The only exception of course if you are swapping between an EGR (California) and non-EGR (49 state) car. And EGR intake into a non EGR car will require a blockoff plate on the intake. A non-EGR intake into an EGR car will "require" you to swap to a 49 state computer or just unplug the vacuum motor wiring harness for the EGR or just leave the EGR components hanging and say "F'it".
But really, the most important thing to remember is "YES, that 89 motor will fit into a 93 MTX"