Silence is Golden by EpicCrab is a cool mod that allows the player to keep the Golden Claw by not giving it to Lucan in the first place. It's useful if you already know that you want to keep the claw. Tundra Homestead for example has a display for all of the claws.

While the original mod is perfect as is, I still made some subjective edits to the new dialogue choices the player has and I am sharing them here.

It changes "(Lie) I killed the bandits, but I didn't find the claw." to "I killed the thieves, but I didn't find the claw. (Lie)".
I made the edit because the vanilla game places the "(Lie)" at the end of sentences. This sentence is from the vanilla game for example: "There's a horse waiting at the stables. I'll make sure you're safe. (Lie)".

I also replaced the word "bandits" with "thieves", because Camilla and Lucan both only mention thieves in their dialogue and your character never tells them that there was a whole group of bandits at Bleak Falls Barrow.

It also changes the version of the dialogue that comes up when you first do Bleak Falls Barrow and then go to Camilla and Lucan.Now when Lucan tells your character about the claw and how it looks, you can simply answer "Sorry, I haven't seen it. (Lie)", instead of telling them that you killed the bandits.
Telling them that would basically confirm that you did find the Golden Claw. How else would you know you killed the right people, if they didn't tell you where the thieves went yet?

I want to thank EpicCrab for the original Silence is Golden mod, which is of course a requirement.