Firstly, I don’t think that you’re going to find any online mapping software that produces bike-specific routes. There just isn’t the demand. You may be able to find a commercial package for which you can set a requirement that freeways be avoided, but the one I use (Microsoft Streets & Trips 2001) doesn’t have that feature.
In the days before mapping software, people used things called maps. If they on a bike and risked running into major elevation changes, they used Topographic maps. For a bike trip, you need to figure out if you can do it in a single day (it’s over 120 miles in this case). If not, do you have any preference as to where you want to spend the night on the way? North of Everett, you’ll be going along old highways (bypassed by the Interstate) with food/lodging opportunities less frequent. What kind of shape are you in? Is there anything specific you want to see?
Ideally, you want to find people who’ve done the trip before. Try contacting a Seattle-area bike club, or going to your local library. Those resources will be better able to tell you if there are bike paths along any of the route you want (I tend to think that there won’t be outside the immediate Seattle area, but I’m willing to be corrected on that!)
However, I can at least plan you a basic route using MS Streets & Trips, if we assume that you can bike along any highway that is not an Interstate (which I believe to be the case). By setting various off-Freeway specific waypoints on the route, one can cause the software to avoid the Freeway (I-5 in your case). With a little bit of playing around, I’ve generated a bike-possible route from Shoreline (WA) City Hall (right near Aurora Ave N. at N.175th St) to the main Anacortes Ferrry Terminal. The route comes out to be 121.6 miles; this is slightly further than it would be if you could use the freeway.
[li]Head North on Route 99 (called Aurora Ave N, then Pacific Highway, then SW Everett Mall Way, then SE Everett Mall Way, then Broadway). After about 30 miles, you’ll be in on Broadway in Downtown Everett. Good place to stop, rest, and eat.[/li][li]Out of Everett, Broadway becomes Route 529. Stay on this going North into Marysville (about 40 miles from your starting point), where it becomes State Ave, then Smokey Point Blvd.[/li][li]Turn left onto Route 530 when Smokey Point Blvd dead-ends into it (53 miles from your start)… You’ll stay on 530 for the next 28 miles as it wiggles its way through marshland, until you reach Conway (~81 miles from your start).[/li][li]At Conway, take Conway Road, which runs alongside I-5, and turns into Old Highway 99 S, until you reach the city of Mount Vernon (take S. 2nd St, S. 3rd St, Kincaid Ave, then Cleveland Ave to get into the city center). You’re now 93 miles from your start. Good place to eat, rest, spend the night.[/li][li]Refreshed, take Route 536 westward out of town (W. Division St, turns into Memorial Highway). This will merge with Route 20 (still going west) for the final few miles to Anacortes. You’ll hit the motel strip on Commercial Ave (the last mile or so into Anacortes proper) at about 114 miles from the start.[/li][li]If you’re heading out to the ferry for the San Juan Islands or Vancouver Island, you’ve got another 8 miles or so of pedaling on Route 20 still to go.[/li][/ol]
That’s a fairly flat ride (certainly once you’re north of Everett). Good luck!