Dear Zinovy,
Apologies for the long delay in addressing this question! So the answer is that we are working to set up an efficient cross-match service, with which you could upload your catalog into your personal database, cross-match it against e.g. the NOAO Source Catalog, and include the measurements in your table. For the moment, a slow but workable approach is to read the file into a Jupyter notebook and loop through the objects to find the closest match (or matches) to each one. Here's how to do that:
1. Log in to Data Lab
2. Start up the notebook server
3. Upload your catalog file through the notebook interface
4. Read the catalog from the notebook
5. Use the q3c_radial_query database function to find matches for each object, one at a time
6. Write the result to the notebook space
7. Use the notebook interface to download the file.
If you would like, I can send you a notebook that would do this against the NSC catalog.