Bismillah,
Yes, you should say Salam regardless. The Prophet (PBUH) when he used to send letter to the kings inviting them to Islam, he would include greetings in the letters. Here is an example: (This letter was sent to Heraclius the king of Byzantium)
بِسْمِ اللَّهِ الرَّحْمَنِ الرَّحِيمِ . مِنْ مُحَمَّدٍ عَبْدِ اللَّهِ
وَرَسُولِهِ إِلَى هِرَقْلَ عَظِيمِ الرُّومِ . سَلَامٌ عَلَى مَنْ
اتَّبَعَ الْهُدَى . أَمَّا بَعْدُ ؛ فَإِنِّي أَدْعُوكَ بِدِعَايَةِ
الإِسْلامِ ، أَسْلِمْ تَسْلَمْ يُؤْتِكَ اللَّهُ أَجْرَكَ مَرَّتَيْنِ ،
فَإِنْ تَوَلَّيْتَ فَإِنَّ عَلَيْكَ إِثْمَ الأَرِيسِيِّينَ (أي أتباعه
ورعاياه الذين يتابعونه على الكفر) . وَ [ يَا أَهْلَ الْكِتَابِ
تَعَالَوْا إِلَى كَلِمَةٍ سَوَاءٍ بَيْنَنَا وَبَيْنَكُمْ أَنْ لا
نَعْبُدَ إِلا اللَّهَ وَلا نُشْرِكَ بِهِ شَيْئًا وَلا يَتَّخِذَ
بَعْضُنَا بَعْضًا أَرْبَابًا مِنْ دُونِ اللَّهِ فَإِنْ تَوَلَّوْا
فَقُولُوا اشْهَدُوا بِأَنَّا مُسْلِمُونَ ]
“In the Name of Allaah, the Most Gracious, the Most Merciful. From Muhammad the slave and Messenger of Allaah to Heraclius the ruler of Byzantium. Peace be upon those who follow true guidance. I call you with the call of Islam. Become Muslim and you will be safe, and Allaah will grant you a two-fold reward, but if you turn away, upon you will be the sins of the Areesiyyeen (peasants i.e., his followers and subjects who would follow him in kufr).
‘Say (O Muhammad): “O people of the Scripture (Jews and Christians):
Come to a word that is just between us and you, that we worship none
but Allaah (Alone), and that we associate no partners with Him, and
that none of us shall take others as lords besides Allaah. Then, if
they turn away, say: “Bear witness that we are Muslims”’
Reference:
