Schema information within Trigger?
If the effect isn't required until a later point in time, I would execute the payload at that later point in time and not via trigger. This way you can collect multiple updates on the underlying table and avoid redundant calls of the DDL script.

Depending on your circumstances, a timestamp column or simple boolean flag in the underlying table might suffice to mark rows that should trigger delayed events.


  is it possible to obtain the current schema from the underlying table ..


Yes. You can query practically any possible detail from the system catalogs or from the standardized (but much slower) information schema.  Furthermore, in a trigger procedure you have the TG_TABLE_SCHEMA variable set.

This related answer has more information and an example:
How do I list all columns for a specified table