Aside from comment, this is assuming your "ID" columns are integer based and not string, don't try to convert them.
Also, to help optimize the query, I would ensure you have indexes
External_Transactions ( acct, event_id, cancel_evt_id )
Transaction_Type ( transaction_type_id, transaction_type_class )
Transactions ( transaction_evt_id, acct, asset_id, cancel_flag )
Transactions ( cancel_evt_id, acct, asset_id, cancel_flag )
SELECT
et.event_id,
et.cancel_evt_id
FROM
external_transactions et
JOIN transaction_type tt
ON et.transaction_type_id = tt.transaction_type_id
AND tt.transaction_type_class != 'XYZXYZ'
LEFT OUTER JOIN transactions t1
ON et.event_id = t1.transaction_evt_id
AND et.acct = t1.acct
AND et.asset_id = t1.asset_id
AND t1.cancel_flag = 'N'
LEFT OUTER JOIN transactions t2
ON et.cancel_evt_id = t2.cancel_evt_id
AND et.acct = t2.acct
AND et.asset_id = t2.asset_id
AND t2.cancel_flag = 'Y'
WHERE
et.acct = 'ABCDEF'
AND ( t1.transaction_evt_id IS NULL
OR t2.cancel_evt_id IS NULL )
You might even benefit slightly if the transaction table had an index on
Transactions ( acct, asset_id, cancel_flag, transaction_evt_id, cancel_evt_id )
and the left-join was like
SELECT
et.event_id,
et.cancel_evt_id
FROM
external_transactions et
JOIN transaction_type tt
ON et.transaction_type_id = tt.transaction_type_id
AND tt.transaction_type_class != 'XYZXYZ'
LEFT OUTER JOIN transactions t1
ON et.acct = t1.acct
AND et.asset_id = t1.asset_id
AND (
( t1.cancel_flag = 'N'
AND et.event_id = t1.transaction_evt_id )
OR
( t1.cancel_flag = 'Y'
AND et.cancel_event_id = t1.cancel_evt_id )
)
WHERE
et.acct = 'ABCDEF'
AND t1.transaction_evt_id IS NULL
In both cases, the indexes would be COVERING indexes so it did not have to go back to the raw data pages to confirm other elements of the records