There is no guidance for going the route you delineated.
If you want to make a distribution and issue K-1s there is guidance if beneficiaries will not provide their SSNs.
First of all, failure to provide an SSN in that circumstance can result in penalties under Section 6721. Further, the trustee (or executor) must send the beneficiariy a W-9 and then document attempts to obtain the SSN. There is also the possibliity of backup withholding.
See also https://ttlc.intuit.com/community/taxes/discussion/what-do-you-do-when-trust-beneficiaries-refuse-to...
