Yes, just changing planes in Frankfurt counts as a transit. Even transit on land (e.g. by car, train or bus) is exempt from the requirement to register. So no, you do not have to register.
You will find this confirmed on the very first page of the entry registration form:
When do I not need to provide my details?
- If you ... are only passing through Germany.
The wording of the regulation (in its official English translation):
Section 3 (obligation to register) ... does not apply to persons who
... are only passing through the Federal Republic of Germany and will
be leaving the country by the quickest route to complete their
So as long as you are not planning an unnecessarily long stay in Frankfurt, e.g. to take a trip into the city or something like that, and are just entering to wait for your onward flight, you clearly fall into this exception from the obligation to register.
The last time I travelled from Sweden to Germany, about 5 weeks ago, I was asked at check-in wether I was going to stay in Germany or was just entering for the purpose of transit. Since I was going to stay, they wanted to see my entry registration. I would very much assume that also the check-in staff at the airport in Stockholm is aware of the difference. If they for some reason are not and demand to see an entry registration, you can always do that at the airport. It only takes a few minutes, but you do in that case indeed need to 'invent' an address, at which you are going stay in Germany.