Your specs/mobo/case etc would be relevant here to give you any idea.
Since you don't want a backplate, it might be reasonable to assume you have a pre-built Dell or HP, which secure the stock cooler directly into the case itself - if that's the case, the only way to install another cooler would be to remove everything from the case & transplant it into a new one (which can be easier said than done, and will take you over your 30EUR budget).