No. A Decker/Technomancer PC or NPC is not required to play SR5. I definitely recommend one though, and if you want to play a Black Trenchcoat game, you have to have a hacker for some runs. No way around it.

I have personally dealt with this issue in my own SR5 campaigns. You have three realistic options that won't inconvenience PCs by forcing them to put Karma into unwanted computer skills.

• Make a Decker/Technomancer GMPC that the players can hire to take along with them on runs. While you make clear in your question that you have considered and rejected this approach, I mention it because ultimately this is the solution I decided to use. Your mileage may vary. I chose to build a cybered-up Technomancer who could fight well in meat-space and used his sprites to hack in the background so he wouldn't slow down or hamper the group with unnecessary Matrix actions. He's expensive to hire, but when the team needs a hacker, he's reliable and he gets the job done.
• Make a Decker/Technomancer GMPC that the players can hire. At first, this may seem identical to the first option. The crucial difference is that if you don't plan on the PCs actually bringing the hacker on the run in question, he doesn't need fully fleshed out stats and personality. Simply decide how big his average dice pool is going to be for the major computer skills and you're done. The important thing for the PCs to keep in mind is that they need to have the hacker do the legwork before they actually start the run. Since the hacker isn't going on the run, he faces far less danger and so you can also charge your PCs less to hire a hacker in this manner than you might have otherwise if you choose. I like to call this the "lazy GMPC" method and when I use it I generally assign the GMPC three values: a small dice pool for actions he is terrible at, a medium dice pool for actions he is passable at, and a large dice pool for actions he specializes in. Computer/Hacking skills will have the large pool, utility skills like Locksmith and Perception will use the medium pool, and then everything else will use the small pool. Small pool might be 3-5 dice, medium pool might be 6-8 dice, and the large pool is usually like 10-12 dice.
• Design your runs so that the PCs don't need a hacker to succeed. You can do this one of two ways: either run a Pink Mohawk style game where the PCs are free to act like action movie stars and simply punch/shoot/blast their way through any obstacles, or have the PCs use social skills such as Intimidate or Con to get people to help them who live or work where the run is to take place. This is similar to hiring a hacker, only more risky since the PCs can never be sure whether they are more intimidating or convincing than the relevant employers or authorities. Philip's answers expand more on this particular solution. In one answer he provides some examples of solid Pink Mohawk play, and in his other answer he gives some examples of run ideas that are light on hacking so your PCs can focus on the action.