Pass HAProxy healthcheck requests as User-agent "LB-Check" to the backend webservers (apache)
you're already requesting what i assume to be a unique file name for the health check, so why do you need something else?
but to answer your question, you can abuse the HTTP/1.0 bit as follows:
option httpchk HEAD /healthcheck.txt HTTP/1.0\r\nUser-agent:\ LB-Check
Few years later and it is supported by HAProxy directly:
option httpchk
http-check send hdr User-Agent "LB-Check" hdr Host example.com meth HEAD uri /healthcheck.txt
https://www.haproxy.com/documentation/hapee/latest/onepage/#4-http-check%20send