Short answer
Can I ride a 45 km/h scooter through the Elbtunnel in Hamburg?
Not through the A7 Elbtunnel. The tunnel is part of the Autobahn, and a 45 km/h scooter isn't allowed on it, however short the stretch.
Not allowed
A7 Elbtunnel
Instead
Roads without the Autobahn sign
Watch for this sign
This blue sign marks the start of the Autobahn. Only vehicles registered for more than 60 km/h are allowed on it, and a 45 km/h scooter isn't (§ 18 StVO).
The A7 carries on north and south of the Elbtunnel. So you'd already be on the Autobahn before you ever got under the river.
Why I built nonstop
I ride a 45 km/h scooter myself and started out with Google Maps. For me, “avoid highways” only avoided them when it felt like it. And there was no way to exclude Kraftfahrstraßen at all.
With nonstop you enter a start and a destination and get the fastest and the shortest route that's legal at 45 km/h. It's free, and there's no account. If a street is wrong, tap it and block it. Or allow it if you know you can ride there, your device keeps both.
Try it on your next ride.
Common questions
How do I get across the Elbe on a 45 km/h scooter?
Not through the A7 Elbtunnel, and not on the HADAG harbour ferries either, since they don't carry motorcycles or mopeds. Put your start and destination into nonstop, and the route you get avoids Autobahnen and Kraftfahrstraßen.