The Silmarillion chapter 1 (of the Beginning of Days) includes the following description of the Noldor:
Aule it is who is named the Friend of the Noldor, for of him they learned much in after days, and they are the most skilled of the Elves; and in their own fashion, according to the gifts which Iluvatar gave to them, they added much to his teaching, delighting to tongues and in scripts, and in the figures of broidery, of drawing, and of carving.
While some of these could be argued to be crafts, the definition of others could really go either way.
There is other evidence elsewhere; letter 156 for example has the following to say about the Númenoreans:
While obedient, people from the Blessed Realm often visited them, and so their knowledge and arts reached almost an Elvish height.
The distinction of knowledge from art, and the lack of capitalization of "art", are both significant. Contrast letter 131:
Their 'magic' is Art, delivered from many of its human limitations...
Here Tolkien used capitalized "Art" to represent magic, power, etc; the lack of capitalization when describing the Númenoreans strongly suggests that something else is being described here, and there is no reason to suppose that it's anything other than artistic works.
We also see the following description of Meduseld (in the Two Towers, King of the Golden Hall):
As their eyes changed, the travellers perceived that the floor was paved with stones of many hues; branching runes and strange devices intertwined beneath their feet. They saw now that the pillars were richly carved, gleaming dully with gold and half-seen colours.
This in turn contrasts with a description of woven cloths containing figures from legend immediately following it, and it seems reasonable to suppose that the colouring and decoration described here was purely artistic.
In Return of the King, Minas Tirith, we also have the throne room described:
Monoliths of black marble, they rose to great capitals carved in many strange figures of beasts and leaves; and far above in shadow the wide vaulting gleamed with dull gold, inset with flowing traceries of many colours.
And once more this description is purely decorative.
So there are descriptions of artistic works present in Tolkien, but they are incidental to the main themes of Tolkien's interest (which were history and linguistics), and while Tolkien may not say anything about other possibilities, that doesn't mean that they don't exist.
I'll leave you with a quote from letter 181:
The Elves represent, as it were, the artistic, aesthetic, and purely scientific aspects of the Humane nature raised to a higher level than is actually seen in Men. That is: they have a devoted love of the physical world, and a desire to observe and understand it for its own sake and as 'other' – sc. as a reality derived from God in the same degree as themselves – not as a material for use or as a power-platform. They also possess a 'subcreational' or artistic faculty of great excellence.
Again, Tolkien doesn't describe the kind of art that the Elves do, but it most certainly does exist.