I've been doing the same thing for about a year now. I copy-and-paste the message below, with a few tweeks as needed for each situation.
"Hi, Hans.

First, thanks for the connection request on LinkedIn.

Replying to your message: I'm a sole proprietor, and I'm not in need of your company's services.

Now, it's time for the reverse pitch. I do computer and network services for many small businesses that aren't large enough to have a full-time, in-house IT staff. I also do contract work for larger companies. My clients include Georgia Power, T-Mobile, and Caltrans. If you have need of IT services, most things can be taken care of remotely.

I hope you'll think of me for your network and security needs. I'd appreciate referrals to other businesses, friends, and family who may need remote IT support.

My phone number is 206-465-2422, mobile and text messaging. Have a great day, and stay safe and healthy.

--Bob Young
FIFO Networks
fifonetworks.com"