Testing from Scala
Now for the fun part - we get to write some Scala!
Now if may turn out that this ends up being the end of the Scala road at your shop, due to restrictive policies about production code. That's a shame, and it could take a very long time to change. I know of one large company where "Java for production code, Scala for tests" has been the standard now for several years. Sure it's not perfect, but it's better than nothing, and developers who haven't yet caught the Scala bug can learn it in their day job.
The tests you write may eventually be the only unit tests for this code, so I would strive for complete coverage rather than merely a copy of the "legacy" Java-based tests. For the purposes of measuring this coverage I can highly recommend the jacoco4sbt plugin which is simple to get going, well-documented and produces excellent output that makes sense in Scala terms (some other Java-based coverage tools seem to struggle with some of the constructs the Scala compiler emits).
In addition to (possibly) getting introduced to Scala and also learning the basics of writing a specs2 test, you might even discover that your code under test is a little tricky to test from this new perspective. This is a good thing, and if it encourages a bit of mild refactoring (while keeping both Java- and Scala-based unit tests passing of course) then so much the better.
Once you've got some solid, measurable coverage from the Scala side (I like to shoot for 90+% line coverage), it's time to commit those changes again, and push them to your CI build. If you haven't already, install the JaCoCo Plugin for Jenkins so you can get pretty coverage graphs on the project page, and even automatically fail the build if coverage drops below your nominated threshold(s).
Switching your Jenkins build project to SBT
Speaking of which, you'll be wanting to adjust your Jenkins job (or equivalent) to push your new, somewhat-Scala-ish artifact to your Nexus (or equivalent). Firstly, for safety, I would actually be duplicating the existing job and disabling it rather than getting all gung-ho with something that can potentially be a very carefully-configured, nay curated Jenkins project configuration.
Luckily this should be pretty straightforward if you employ the Jenkins SBT Plugin - set the Actions to something like clean jacoco:cover publish to get the optimal blend of cleanliness, test-coverage visualisation, speed, and build traceability.
If for any reason you can't use the plugin, I'd recommend using your CI tool's Run script functionality, and including a dead-simple shell script in a suitable place in your repository; e.g.:
#!/bin/bash echo "Running `which sbt`" sbt -Dsbt.log.noformat=true -Dbuild.version=$BUILD_NUMBER clean jacoco:cover publish
Once you've got everything sorted out and artifacts uploading, you'll notice that your Nexus now has a new set of artifacts alongside your old Java ones, with a _2.10 (or whatever Scala version you're running) suffix. Scala in your corporate repo! Progress!