Leontief's Paradox and the amount of capital
Leontief did not use total capital stock for his calculation of capital/labor requirements in the export/import sector. He measured 'requirements per million dollars of exports and imports replacements', and this for various industries (Leontief, 1953, section III, table 2). So he also did not use total capital stock, he used capital requirements AKA capital inputs. 

He did provide summary statistics on the total capital and labor required per million dollars of total output for each industry. This might have confused you. 

Note that he obtained these numbers only after computing them from available data, and he discusses their accuracy in the same section.