I don't usually reply as a Supplier (rather than Advisor), but a possible answer to your enquiry is SfP World Service from Software for People.
SfP World Service is an 'upper end' payroll system, accredited by HMRC, with integrated and fully configurable HR capabilities that can be partly or fully switched off. It can generate HTML payslips that are usually made accessible to employees via self-service browser access (after secure login) to your central database - for viewing and/or printing (from a full history not just the most recent one). However the files could be supplied for loading to a different database if preferred.
As you say, payslips can also be emailed - and there are no stylesheet issues (as these are held at the server end and can therefore easily be created to replicate your payslip style/layout).
If you would like to discuss your underlying requirements in greater detail, please feel free to contact me via
hugo@hrsystems.net