I want to resign with only one week notice period. My employment contract says that you have to give either one month notice or "payment in lieu thereof". I am willing to pay for my notice period. My question is: can this short notice be held against me in case of recommendation or rehiring in future.?
Unfortunately, anything can be held against you in the minds of others. The good news is many employers give out a bare amount of information about your previous employment in their company: dates, job titles/descriptions, and that's about it.
If you use anyone at that company as a reference, just make sure they don't hold this against you. Always know what people are going to say about you before using them as a reference. Don't ask them to lie about your contract situation when asked. The key is this was a mutual agreement of both parties.
If your contract says you can do it, it means they are confortable with you doing that, or… they wouldn't have put such a clause in the contract.
Hence, if they are so unreasonable to "hold this against you", it means they make no sense, they are unpredictable, and they can "hold against you" anything for no reason at all anyway.
Either way, just do it.