Admittedly I’ve always found the IMS LTI documentation a bit difficult to parse, but my understanding is that LTI 1.1 is a superset of LTI 1.0 that enables some additional functionality, and that they establish a connection/handshake in the same way. LTI 1.1 just passes some additional data to the tool.
It may be that your LTI 1.0 courses “just work” with LTI 1.1. (LTI 1.3 is a another matter, and is significantly different)