I am a Muslim and I am thinking about if I said "I swear to/that..." will it be considered as an Islamic oath (like saying (in Arabic) "oqsm b Allah")?
I might need to say that to somebody who is not a Muslim, so I can't use "I swear to Allah".
No you must say i swear to God, otherwise don't swear... whatever your interlocutor.
Note this Hadith from the two sahih (1): "
إن الله ينهاكم أن تحلفوا بآبائكم فمن كان حالفاً فليحلف بالله أو ليصمت و الله تعالى أعلم
God inhibits you swearing to your ancients, But if you do then swear to God or don't swear at all . And Gods knows best