Welcome to the community
I assume that this is a project deployed on mainnet and you want to use OpenZeppelin Upgrades plugins to test and check upgrades.
What version of openzeppelin-eth are you using? It looks like the last Solidity 0.4 version of the upgrade safe fork of OpenZeppelin Contracts was openzeppelin-eth 2.0.2.
I don’t know if there were storage layout changes between versions of openzeppelin-eth or whether you can upgrade to a later version. (For example, storage layout changes means that we can’t upgrade from OpenZeppelin Contracts Ethereum Package 2.5 to 3.0).
My assumption is that you can use the latest compatible version of openzeppelin-eth (this could be 2.0.2) and use the OpenZeppelin Upgrades Buidler plugins but will need to manually configure the network file (https://docs.openzeppelin.com/upgrades-plugins/1.x/network-files#network.json).
Are you able to share a repository with the code that you want to migrate?