Unless illegal in the jurisdiction of your legal headquarters, you should go for electronic signing. It is the 21st century – and just like due diligence is done in a virtual data room, investment contracts should be handled electronically.
While there are advanced solutions such as
DocuSign, a signed PDF version of the final contracts should be good enough (though as always it should be checked with your lawyer). Make sure that you do not just send around an electronic version of the signature page (e.g., page 16 of the SHA) but an electronically signed version of the entire document, and that you do a solid version control in the footnote of all your legal documents.
Your lawyer should provide an electronic closing binder to each new and all existing shareholders at the end of the fundraising round. This binder should contain all signed documents. Accuracy and full transparency are crucial – any shortcut or mistake can hurt you incredibly in the next financing round or prevent an exit.