Where is the shutter squeak produced actually ? In wich part of the mechanism ?
Note the pins - the parts which are connected to the chassis- of the two reeling posts at the left and the two spring loaded cylinders on the right. Apply a very small amount of oil on those pins. From the bottom of the chassis, you can see the pins, and you can apply the oil there.
The squeak can also (and often) originate from the pulleys on the reeling post of the second (narrow) curtain. These pulleys relay the straps of the first (wide) curtain. You can also apply a small amount of oil on the pulleys. Be very careful not to get any oil on the curtains or the ribbons.
If some oil gets on the curtains, immediately remove it with a cotton tipped toothpick (or 'Q-tip') dipped in some lighter fluid. A liberal amount of lighter fluid will not harm the curtains. If the glue used for your Exakta is original, you don't have to worry about lighter fluid getting in them. IHG used shellac, which is quite inert to lighter fluid. The shellac glue is affected only by alcohol or acetone.
While the crate is still out of the chassis, you may want to oil the other parts too. Put a bit between -using the syringe again- the gears of the winding lever.
Put a bit of oil on the pivot of the large gear under the shutter dial as well.
NOTE! When working on the "winding" side of the chassis, BE CAREFUL NOT TO REMOVE the reeled spring under the winder. This can be difficult to replace and synchronise properly with the rest of the mechanism. ALWAYS replace the winder and its retaining nut after disassembling the top cover to prevent the winding spring from popping out.