Try this, basically, you need to tell it if the field is blank to return the empty value.
IF({Trækdato (FarPay)}=BLANK(), BLANK(),
IF(AND(DATETIME_FORMAT({Trækdato (FarPay)}, "D")<10, DATETIME_FORMAT({Dato for udløb}, "D")<10),
IF(WEEKDAY(DATETIME_PARSE(DATETIME_FORMAT({Dato for udløb}, "YYYY-MM-10"),"YYYY-MM-DD"))=3, DATEADD(DATETIME_PARSE(DATETIME_FORMAT({Dato for udløb}, "YYYY-MM-10"),"YYYY-MM-DD"),1, "weeks"),
IF(WEEKDAY(DATETIME_PARSE(DATETIME_FORMAT({Dato for udløb}, "YYYY-MM-10"),"YYYY-MM-DD"))<3, DATEADD(DATETIME_PARSE(DATETIME_FORMAT({Dato for udløb}, "YYYY-MM-10"),"YYYY-MM-DD"),3-WEEKDAY(DATETIME_PARSE(DATETIME_FORMAT({Dato for udløb}, "YYYY-MM-10"),"YYYY-MM-DD")),"days"),
IF(WEEKDAY(DATETIME_PARSE(DATETIME_FORMAT({Dato for udløb}, "YYYY-MM-10"),"YYYY-MM-DD"))>3, DATEADD(DATETIME_PARSE(DATETIME_FORMAT({Dato for udløb}, "YYYY-MM-10"),"YYYY-MM-DD"),10-WEEKDAY(DATETIME_PARSE(DATETIME_FORMAT({Dato for udløb}, "YYYY-MM-10"),"YYYY-MM-DD")),"days")))))
)