Shinano Railway Train ticket question

Hello, I'm travelling from Matsumto to Karuizawa by taking the following trains.

12:30 JR Shinonoi Line from Matsumoto Station to arrive Shinonoi Station at 13:33,
13:38 Shinano Railway from Shinonoi Station to arrive Karuizawa Station at 15:18

It seems Shinano Railway does not accept Suica Card, is it possible to buy their ticket at the Matsumoto Station? Since I only have about 5 minutes for the transit at Shinonoi, I'm afraid I don't have enough time to buy the Shinano Railway ticket there. Can I use the JR Shinonoi Line ticket to do fare adjustment at the Shinano Railway Karuizawa ticket office after I arrive.

Thank you.

No, I think you need a new ticket. Potentially only payable with cash at one of the machines.

"Shinano Railway does not accept Suica Card" - true.
"about 5 minutes for the transit at Shinonoi" - also true, but that is is enough time.
"Can I use the JR Shinonoi Line ticket to do fare adjustment at the Shinano Railway Karuizawa ticket" - You do aa adjustment at the Shinanoi Railway station showing your JR ticket at the manned ticket gate.