No! Don't run into anything. Think what is the real problem. Is it that you don't like dealing with uncertainty?
"I hated doing experiments"
What makes you think that you will not do experiments in "bioinformatics and statistics"? An Experiment does not have to be something done in test tube. People working in bioinformatics and statistics are also doing experiment all the time, they are experimenting with there code and methods. And yes most of the time things do not work. After all it is "Research".
OR is it
I couldn't justify spending years of my life working on a tiny protein
that no one cared about
The bad news is that it is true in other fields also. There are plenty of bioinformatics/statistics methods/papers that no-one cared about (My gut-feeling: such papers are more common in bioinformatics/statistics). No-one can predict what with absolute certainty what what will work and about what people will care.
Bottom line, experiments not working and no-one cares about my research are common in science. If you think that this is the main problem that what is the guaranty that you will not face them in other field? In that case you should also consider option of moving out of academia.
In theory it is possible to switch to subject and it might be easier because fields are linked. But you should not forget the bigger picture and reality. You don't like your current topic, that indicates that might took a ill-informed decision in past. Don't repeat it again. Before taking any decision, talk to your Professor or someone who is experienced and know you well (about your research work). And most importantly talk to a person who is doing bioinformatics/statistics. Someone whose job you want ideally in future. Ask them about the day to day difficulties and challenges. Put yourself in their shoe and then decide.
Note 1: If you want to work as a bioinformatics/statistics technical support then it might be little different (less experiments). But as far I have know people at technical support side of the science are also doing "experiments".
Note 2: As others mentioned, people coming from different field to bioinformatics/statistics, it is true BUT current situation is more different then 10 years ago. As bioinformatics as a field has evolved and matured more and more jobs required more specific knowledge and skills. Although it is not impossible to gain skills but my point is it is much difficult now a days to change to bioinformatics as it was 10-15 years ago when there were very less bioinformatics specific students/phds.