All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The basic principle is that it is prohibited to use the cross and it should be erased or obliterated. This is evidenced by the following Hadeeth. ʻAa'ishah said: “The Prophet, sallallaahu ʻalayhi wa sallam, never used to leave anything bearing a cross in his house but he, sallallaahu ʻalayhi wa sallam, obliterated it.” [Al-Bukhari]
If you need to use these stamps or else you would not be able to send those letters, there is no religious impediment to using them. A prohibited act may be deemed permissible in certain situations acting upon the established Shareeʻah rule, ‘necessities render prohibitions permissible’. Allah, The Exalted, says (what means): {...He has explained in detail to you what He has forbidden you, excepting that to which you are compelled...} [Quran 6:119]
You may obliterate the cross using a pen, for instance, in a way that does not incur any harm on you like obliterating it with your signature using a pen with a different colored ink, if possible.
Allah knows best.