Would it not possibly be easier to cut Indy mentioning 'who was that woman?' in the FBI scene, rather than cutting every mention of Spalko saying her name and rank and even Indy saying her name in the opening ('drop your guns, or colonel doctor Irina Spalko's dead')? It just seems like too many cuts at the start of the movie otherwise, and that could be messy.

Instead, one option would be to just cut Indy asking that one question 'who was that woman?' in the interrogation scene. This would still work:

Ross: Indy, thank God - don't you know it's dangerous to climb into refrigerators, those things can be death-traps.
Indy: Good to see you too, Bob.
Ross: Relax gentlemen, I can vouch for Indy.
Indy: What's going on? Russian soldiers on American soil? *Cut Indy's 'who was that woman?' here *

Perhaps then have a close-up shot of the FBI men, or General Ross, or even a wide-perspective shot, before cutting straight into the document on Spalko being thrown down onto the table and Ross telling Indy about Spalko, and the Kremlin's missions regarding paranormal artefacts. This way, it would still flow - after Indy asking 'what's going on?', he is now being told further information about Spalko, and this makes sense. Even his 'yep, that's her' remark would still be in place in this scenario.