My first college degree was a BFA, with a double concentration in ceramics and metalsmithing/jewelry, so I do have some background here.
I don't have a problem using 'construct' to refer to small scale objects such as jewelry or small containers. However, a term we used most frequently was 'fabricate', regardless if it was jewellery or a container. It does carry an implication of an individually hand-made creation, so I wouldn't use it for anything mass-produced.
Of course other general verbs work such as 'create' or 'make'. Alternately, if you have knowledge of the specific fabrication technique, you could use the corresponding verb such as 'solder', 'raise', 'chase', 'enamel', 'weld' etc., but many objects often employ multiple techniques.
For example, the basic form of handmade metal dishes and bowels is created by the raising process - hammering over various metal or wooden stakes. Commercially they're usually spun, stamped, or pressed.
The process of decorating with stones or jewels is referred to as 'setting' - bejeweling is a vague and nebulous layman term.
However, I most often refer to 'making' a particular piece.