Could you be more clear on what you are looking for and why Electrum can't help you with it?
I don't understand the part where you say that there isn't performance on PoW, nor what you mean by a wallet you get to "work" on.
Do you just want a wallet that can send and receive bitcoins? Then Electrum would do the trick.
I'm trying to make some optimizations on a lightweight client if possible and right now my focus is on optimizing the PoW function.
However, my observation and understanding is that Electrum does not perform PoW but only helps to verify it.
Will like to know if there is any other lightweight client that can meet my criteria.
Well doing a PoW function would be called mining in Bitcoin. Optimizations in mining is a huge thing, worth millions with very big players in question.
Mining isn't even done with computers anymore, it is done by specific machines that do the job a lot more efficiently, called ASICs.
They use their own software, as far as I understand or a full node like Bitcoin Core. I doubt that they use a light wallet, as light wallets are usually for an average user that doesn't want to trade his hard disk space for higher security. Light wallets like Electrum don't verify transactions, they can't as they don't have past transactions and would always require a full node to connect to in order to ask if the transaction is valid or not.
