How do I send Bitcoin from my cold wallet to a new one? I have the public/private keys for my cold wallet. I want to move it all into an Electrum wallet. I understand that I should send my entire balance at once. What medium should I use to make this transfer? I do not want to use Mycelium or any phone based wallet.

Side question: If I want to be able to spend small amounts of Bitcoin on purchases what is the ideal wallet setup I should be using?
Funds from a cold wallet need to either be imported or swept (for cybersecurity reasons sweeping is always preferred over importing) into most any hot or warm wallet to then sent to another cold wallet address synthesized from private keys that are usually in either the Wallet Import Format (WIF) or in BIP 38 standard format (is AES encrypted and starts with the letters 6P). Wallet imports or sweeps usually take WIF or BIP 38 input formats that have associated input error checking versus raw hexadecimal that a prone to human input errors like Ethereum.

Electrum is not technically a cold wallet unless the Electrum BIP 39 seed words have never been loaded into an Electrum warm wallet.  An Electrum wallet is warm only if it uses a hardware wallet such as a Trezor, Ledger or Keepkey token generators that have been loaded with BIP 39 seed words. Otherwise, the Electrum wallet is a hot wallet.

Cold wallets need the private keys and associated public addresses generated on a trusted offline computer. Cold wallets can use self contained JavaScript programs, or a standalone binary executable such as Bitcoin-Explorer (bx) running on air gapped computers that can also leverage brainwallets provided the brainwallets input text have sufficient entropy.

To answer your side question, you should be using a HD hardware token generator with Electrum to have warm wallet functionality, or you need to use multiple cold wallets probably using a trusted JavaScript key generator program, not a single cold wallet.