To answer the principal question in the body: yes, this would violate any such applicable patents. A patent provides the legal right to "exclude others from making, using, selling, offering for sale, or importing the patented invention for the term of the patent". Note that although some of those activities are implicitly commercial, others are not; making and using are both controlled, whether or not they are done for profit. Creating and distributing a 3D model is an interesting approach, the details of which I'm not qualified to consider, but even if it doesn't leave you in infringement it will leave your end-users, if they use it to make an item which embodies one or more valid patents, in infringement of those patents. It is not kind to publish such designs without very clear warnings.
To answer the question in the title: yes, and you may do so without putting yourself or your end users in harm's way, provided you own the patent or have a licence so to use it.
To answer the unasked question in the body: the usual lifetime of a patent is 20 years. If this one was granted in 1997, it may well now be expired. You should probably dig a little harder on that front. And as ever, IANAL/IANYL, so don't rely on this opinion without taking professional advice.