Running WordPress/CiviCRM without cron?
Yes, you can run CiviCRM on a host which lacks cron functionality. CiviCRM's scheduled tasks can be triggered by HTTP requests made to CiviCRM from anywhere, so you have lots of options.

To do this, you configure cron according to the documentation based on the instructions for using cron via the "URL method".


CiviCRM cron setup documentation (wiki), URL method
CiviCRM scheduled jobs documentation


Do research your options for your existing host fully - you're best off with "proper" cron support if it's available to you, since a simpler setup is going to be more robust. But, if your hosting provider really lacks support for cron, you have other options like:


Any always-on machine which has cron (including an office mac, or a raspberry pi, or your office NAS or home PVR). UNIX is all around you!
Hosted cron services like easycron.com
A Windows scheduled task will do it (adjust Drupal instructions to suit), provided that machine will stay on.
I heard once of someone setting their cron URL as an RSS feed in their browser, so the browser would trigger it with each update ...


Not recommending that last approach  — just mentioning because it shows how you can work around this with a little ingenuity ...

If you do use an external server, beware of forgetting about that cron task - for example if you one day stop using the laptop that's telling CiviCRM to send your emails!

All that said, my recommendation is to select a hosting provider which supports your software well, rather than select your software to suit constraints of any given hosting environment. If your host doesn't support core CiviCRM functionality without some outside help, what results could you expect for successful campaigns and advanced functionality in future?