Careful there - there is no evidence the original poster is or is not in the United States. The right to public exercise your faith is not uniform around the world.
If someone feels making the sign of the cross would subject them to unfair treatment, persecution, etc. or would make those around them uncomfortable - that is a determination that person needs to make for themselves. They have to live with all the consequences of their actions, so they should let their conscience be their guide.
There is no rule, rubric, or teaching I have ever heard that stipulates prayer must begin with the sign of the cross. Many formalized rituals begin with the sign of the cross, and the sign of the cross is a prayer in and of itself. Many rites and rituals do have a stipulation in their rubrics stating when the sign of the cross should be used in that rite/ritual but to claim every instance of prayer must begin with the sign of the cross is not correct.
Given a choice between just not praying, or not beginning a prayer session with the sign of the cross, I recommend the latter.