My apologies for missing your request. The 1787 version on his website appears to be a variant of the 1760 edition, or the 1787 Dutch version. There were different English translations:
- 1760 London
- 1777 London (there is much debate about this one existing)
- 1787 Dutch
- 1787 New York
- 1793 London
- 1797 London
I am fairly certain old English Latin Alphabet variants of typesets were dropped shortly after the Revolutionary War in the United States. As such, no Vattel translations printed in the United States should have the old English Latin Alphabet typeset shown in the example you provided.
England and Europe were still using this typeset and alphabet well into the early 19th century.