The Prophet salla Allahu alaihi wa sallam used to shorten prayers when he travelled and pray everything normally with the exception for the Sunnah prayers of Thuhur, Maghrib and Isha. These are 10 rak’ah he didn’t pray while travelling; 4 before Thuhur, 2 after Thuhur and 2 after Maghrib and Isha.
This means that he offered night prayers, Witr and the Sunnah of Fajr.
Therefore, a traveler only skips the above mentioned Sunnah prayers and prays everything else normally such as Duha, Istikhara etc.