Firstly, "squawk" is so spelled. There is essentially no difference in service provision on a basic service for discrete or conspicuity codes. With a discrete code you will be identified, but that is it - there is still no surveillance derived traffic information (or at least, there shouldn't be). If you want a traffic or deconfliction service then you have to be identified and you will probably be given a discrete squawk. Note that transponder carriage is not mandatory for these services and the controller can identify aircraft using the PSR if required.
Bear in mind that some units have conspicuity codes that look like discrete codes - just one of their octal block is allocated for basic service use (or whatever) and may be assigned to more than one aircraft. When mode S really takes hold, then the aircraft ID will be taken from the downlinked parameters (already is in some units) and the flight may be identified on surveillance equipment this way, with some provisos.
I'm not sure why you would want a discrete squawk particularly, and there is no standard RTF that I'm aware of for this purpose. A controller issuing a squawk will only ever give an appropriate one (mistakes aside) so I think maybe you're over-thinking this one. Has there been a specific instance that has sparked this question?