Extract the .nif mesh from the meshes.bsa and place it in the Data\Meshes\xxxxxx\xxxxxx\...(keep the same folder structure as it is in the bsa file and create new folders if needed). Rename the .nif file (give it a name like MyInn_custom.nif). Do the same for the textures (MyInn_custom.dds) and place it in the Data\Textures\xxxx\xxxx\... keeping the same folder structure as it was in the Textures.bsa.
The next thing you'll need is Nifscope.
Open the MyInn_custom.nif in Nifscope. In the Block List box, expand the BSFadeNode and then expand NiTriShape. In here you'll find BSLightingShaderProperty. Expand it as well and you'll find BSShaderTextureSet. Click on it.
You'll now see information in the Block details box. This is where you'll have to change the texture from the original to your new textures. Just double click and change the xxxxxx.dds to MyInn_custom.dds (providing you kept the same folder structure). If you created a new normal map texture, change it here as well by clicking on the file xxxxxx_n.dds and put in your MyInn_custom_n.dds. Save the new .nif file.
Back in the CK, create a duplicate of the Inn sign. Rename it to whatever you want and then double click on it. Where it says Model, you'll see a long box with an Edit button at the right hand side. Click Edit. In the box that appears, click Edit at the top and browse to your MyInn_custom.nif. Select it and Open. Click OK twice and your new model is ready to be used in the CK.
Don't forget to add the new textures and meshes if you're publishing the mod.
[Edit]
Forgot to add link to Nifscope -
http://sourceforge.net/projects/niftools/files/nifskope/
The latest version is at the top.