10k products, use SQL. EAV just muddies the waters. Per question is Fastest way.
Find attribute_id
SELECT * FROM eav_attribute where entity_type_id = 4 and attribute_code = 'YOUR_ATTRIBUTE_CODE_HERE'
Update with found attribute_id
from above query.
UPDATE catalog_product_entity_int SET value = 1 WHERE attribute_id = FOUND_ATTRIBUTE_ID
I suppose you could do a subselect with update but for simplicities sake two SQL queries is easiest to grasp.
NOTE: entity_type_id = 4
is most always the product EAV entries. In case you are needing to mass update category or customer attributes this will differ as well as the table that is updated based on what type of attribute it is your updating. Also if you have multi-store setup be sure and note and condition store_id