Even today I still visit websites with no way whatsoever of contacting the webmaster or admin of the said site. It’s frustrating and off-putting and can cause visitors to surf away if they can’t find a way to get in touch. I’ve done it myself!
Most websites are built on the WordPress platform, and it’s very easy to add a secure contact form somewhere on the site. Even if you don’t use WordPress, there are plenty of secure forms you can add, you don’t have to have your eMail address anywhere, just use a contact form or helpdesk. Heldesks are good as you can usually input FAQ’s or knowledgebase questions so members can search for an answer before contacting you directly.
In short, you should really have as many contact options as you can – i.e. your Skype username or number, WhatsApp or Hangouts info etc. The more ways you have for people to get in touch, the more likely they are to trust you.
One more thing – make sure you have your prices visible somewhere on your site. If I find a site where you have to contact the webmaster for pricing, it’s a red flag to me (perhaps they are very expensive). I tend to go looking for something a bit more open as it seems to me they are less likely to have something to hide!