You should upgrade to the latest version of .NET that’s supported by Exchange first and then immediately upgrade to the current CU
Update: Per February 13th, Microsoft updated upgrade guidance on the Exchange Supportability Matrix page, stating:
“When upgrading Exchange from an unsupported CU to the current CU and no intermediate CUs are available, you should upgrade to the latest version of .NET that’s supported by Exchange first and then immediately upgrade to the current CU. This method doesn’t replace the need to keep your Exchange servers up to date and on the latest, supported, CU. Microsoft makes no claim that an upgrade failure will not occur using this method, which may result in the need to contact Microsoft Support Services”.
This means you will be supported when upgrading in the revised upgrade path, but the risk is still there. In the example above, when going from Exchange 2013 CU6 with .NET 4.5.1 to CU19, the support statement indicates you can upgrade to .NET Framework 4.7.1, when install CU19. However, things might break and you may need to contact support to get back in a supported, working situation. Therefor, I repeat my recommendation to download and archive CU’s and .NET Framework files, even when you are not planning on installing them (yet).