Born in San Sebastián, Gipuzkoa, Spain, Cuyami managed ten scoreless La Liga appearances for Real Sociedad after growing in its youth system.
[1] In 2004, Cuyami returned to the Basque Country for his final three seasons, with SD Lemona and Zarautz KE, the latter in the regional championships.
[2] As Javier Balboa, Rodolfo Bodipo or Benjamín Zarandona, Cuyami was the son of Equatoguinean immigrants in Spain, and opted to represent his parents' nation internationally.
His debut came on 11 October 2003 in a 1–0 win against Togo for the 2006 FIFA World Cup qualifiers (eventual 1–2 aggregate loss), in Bata.
Cuyami won a total of two caps, the second coming also that year in a friendly with São Tomé and Príncipe.