How to change the "skin" of an object

For this particular piece it would be perfectly doable without even requiring an actual source photo. You'd simply rebuild it completely artificially with the photo merely providing a reference or a basis for the non-wooden parts. Pretty much anything in there could be faked with a bunch of  simple layers bent and squeezed into place to provide the higlights and shadows and then all you would need in your document is some path or layer mask that provides the contour which can then be cut out after the photos have been treated with a Bulge effect to create some curvature. You would need to find some better source images, though. Your parquet/ block wood image is blurry and has notable lens abberations plus overall it would likely not provide enough resolution to extract soem sections with a nice wood grain pattern.

Mylenium

As Mr. Pfaffenbichler said, some images would help a lot. If you don't want to use 3D, your options are extremely limited, though. Since PS has no consistent warping/ distortion toolset, fitting such stuff after the fact will always be a pain and require a lot of work.

Mylenium

Please post the images in question. 

You must limit texture to object using selection, actually mask and perhaps to use blending modes to apply new texture to object.

In short, create selection of object then use it to create mask on layer with new texture which should be on layer above image with vase. Try using blending, opacity and/or advanced blending modes to create realistic new texture for object (vase).