I believe that most of these fluids must be contaminated by trace amounts of blood in order to become infectious. In this paper, virus was not found in acute phase sputum, tears, vomit, or sweat, and only 1 of 8 saliva samples tested positive for infectious virus. Some of these samples tested positive by RT-PCR, but that does not differentiate between live virus and nucleic acid from inactive viral particles. True, sample sizes are small. I have not seen a study that systematically addresses the question of infectivity of various bodily fluids (that isn't to say there is no such study--if there is one, I would love to see the reference).
Given that so few virus particles are necessary to establish an infection, infection control measures must be strict and thorough to prevent transmission.
There is only one problem. In the wild, outside the clinical environment people are going to be coming into contact with fomites in an epidemic, without knowing they are in an environment where contamination has taken place.
They will not be following currently recommended infection control guidelines for viral hemorrhagic fevers.
While risks might be low for clinical personnel in a clinical (PPE) environment, the general public in the vicinity of the infected person as they become symptomatic will be at risk.
It is what happens before they get in the door that will determine how widespread the disease will become.