  Hybrid networks, i.e., networks that leverage different means of
communication, become ever more widespread. To allow theoretical study of such
networks, [Augustine et al., SODA'20] introduced the $\mathsf{HYBRID}$ model,
which is based on the concept of synchronous message passing and uses two
fundamentally different principles of communication: a local mode, which allows
every node to exchange one message per round with each neighbor in a local
communication graph; and a global mode where any pair of nodes can exchange
messages, but only few such exchanges can take place per round.
  A sizable portion of the previous research for the $\mathsf{HYBRID}$ model
revolves around basic communication primitives and computing distances or
shortest paths in networks. In this paper, we extend this study to a related
fundamental problem of computing compact routing schemes for near-shortest
paths in the local communication graph. We demonstrate that, for the case where
the local communication graph is a unit-disc graph with $n$ nodes that is
realized in the plane and has no radio holes, we can deterministically compute
a routing scheme that has constant stretch and uses labels and local routing
tables of size $O(\log n)$ bits in only $O(\log n)$ rounds.
