In fact, the best way to disguise Thalassa's true nature is to make lesser versions of her, 'space marines' to her Primarch.
Get her to finish the design of the modular cybernetic framework she was originally working on.
Have a few psykers trained as Tech Priests.
Install the modular framework in them.
Build them modular implants
Teach them the Rite of Incarnation and have them use that on their implants
They won't be able to shapeshift to form their implants, they'll have to keep them in secure storage and have them physically removed and installed when they want to switch.
Ideally, Enlighten them so they can fuel their psyker powers with essence rather than drawing on the Warp.
If a couple of them are present when Lorgar and the Emperor meet, then any questions about Thalassa are already answered. She's just a superior model of the same thing.
Doing this is also validation of Lorgar's speech, as here are examples of more people following in Thalassa's path.
Edit: and make a point of using the same Colchisian word for demigod that Lorgar used in his speech to describe them and other people augmented to a similar degree.
We are leaving out some steps that he would ask about and which would give the game away.
"What materials did you use?"
*Describes Moonsilver*
"How did you make that?"
"Father made it with Enuncia, he taught me, wanna see?"
*Emperor clears three months of his schedule to meet Fan Morgal*
Even just that we speak it was already close to the line, that we taught it to Lorgar and together made some kind of super-tech priest described as 'demigod' is I think way over it. We are going to have to come as clean as we can and hope the threat of... Fan killing him dead combined with the sincere offer of alliance is enough to make him play nice. We have seen in the interlude that he is capable of some amount of that. He even showed weakness to his closest companions.
I think that's potentially suicide. It's throwing ourselves on the mercy of the Emperor and hoping that he feels kind that day.
Yzarx has confirmed that we can hide what we are from the Emperor, I think. We can't hide the consequences, so we need other explanations, but I believe we can hide who did them and quite what happened.
Why would Lorgar have to mention Moonsilver, for example? Why would he think to ask, when if asked about Thalassa Lorgar can just point to someone with the augments I mention above and say that she was the trailblazer for this style of augmentation*. Why would the Emperor ask Lorgar what a highly augmented tech priest's implants were made of? He already knows what bionics are made from. He wouldn't have any reason to know she was a shapeshifter, so would have no reason to ask a leading question.
* This would be completely true, and totally derails the subject.