What worked for me is the stunnel with the following configuration:
[local-open-port]
client = no
cert = stunnel.pem
accept = 127.0.0.1:443
connect = 127.0.0.1:9876
[redirect-to-bigip]
client = yes
accept = 127.0.0.1:9876
connect = ...:443
Just change the ... to your BIG-IP device address. Once done you can configure the iRule Editor to connect to localhost on port 443. It works because stunnel will create two different connections (full proxy?), what will also permit two distinct SSL negotiations, one that will work for the iRule Editor and another for the BIG-IP device.