What should one do after performing the Istikhara prayer when no inclination toward either of the two options (traveling between two countries) appears, and the questioner fears making a rational decision that might open the door to satanic whispers?

You have followed the Sunnah by performing Istikhara. There is no harm in consulting wise people and those who wish you well. If you decide to travel, then proceed with it. If it is good for you, Allah will facilitate it for you, and if it is bad, He will divert you from it. This is how the result of Istikhara manifests.