Can a pilot rated in one category solo in another category without a current flight review?
You do require a flight review, per the Beard (2013) interpretation:


  Finally, you have also asked whether a person operating in solo flight
  under a § 61.31(d) endorsement must comply with the flight review
  requirements in § 61.56(c). With a few listed exceptions, no person
  make act as pilot in command of an aircraft unless within the previous
  24 calendar months that person completed a flight review with an
  authorized  instructor. 14 C.F.R. § 61.56(c). Section 61.56(g)
  provides an exception for student pilots provided the student pilot is
  undergoing training for a certificate and has a current solo flight
  endorsement as required under § 61.87. Because this exception applies
  to student pilots, a pilot who holds a higher level pilot certificate
  and has an endorsement for solo flight under § 61.31(d) must comply
  with the flight review requirements in § 61.56 before acting as pilot
  in command of any aircraft.


Regarding the student pilot exception, others have suggested in comments that you are in fact a student pilot because you're new to the category/class. However, the interpretation says you are not:


  Section 61.81 states that subpart C "prescribes the requirements for
  the issuance of student pilot certificates, the conditions under which
  those certificates are necessary, and the general operating rules and
  limitations for the holders of those certificates." As such, by its
  express language, subpart C to part 61 applies only to those persons
  who are seeking or hold a student pilot certificate.


So, since you will be acting as PIC and none of the exceptions in 61.56 apply, you need a flight review. As for a checkride, the person taking the checkride is acting as PIC (61.47(b)) so again, you would need a valid flight review.