You would need to delete your records in a different way than using Airtable’s built-in delete function. You would need to mark your records for deletion in some way.
For example, you could check a checkbox that indicates that you want to delete a record, or you could set a single-select field that says something like “Delete This Record”.
Then you could use the API to search for those records that you’ve marked, and then use the API to delete the appropriate records from both bases.
I’m not sure how you’re using the API, but you could use Airtable’s built-in automations to (1) run a script as soon as you mark the records for deletion, or (2) search your records on a schedule for marked records, and then run a script.
You can also use an external automation tool like my personal favorite Integromat to either:
Immediately delete as soon as you mark a record.
Search for your marked records on a recurring schedule.
These 2 options are the same options as Airtable’s automations, but no scripting required: