I personally feel that as long as the fit up is good, you could go ahead with just calling them fillets for the mid-section rail. Most of it will most likely be ground off and blended anyhow. But, if your just looking for a blanket statement to cover your butt, then you could state that the welds are in compliance with "AWS D1.1 Visual Requirements of TBL. 6.1". And , I would think that your procedures and welder certs have already been reviewed and accepted. Your only about .020" away from being out of scope of D1.1 for material thickness and I don't think pipe for handrail would or could be considered sheet steel.
Your WPS (if you really had to have one for handrail) should be for a fillet welded T joint (Tubular), max. single pass fillet of 3/16", all positions w/low/hy; verts up & dwn. But, I don't see where anything other than someone who is unaware or a completely anal retentive inspector would make an issue of this. But, you just never know, do you.
While you're getting a lot of good common sense opinions here, I think what you're looking for is a technical response that can't be disputed by some customer's inspector who is a real stickler for details.
If you want to get real technical about it, D1.1 does not have a pre-qualified procedure for this joint because it is actually a TKY connection that has to be qualified by a PQR and your welders would have to qualify with a 6GR WPS.
This is one of the reasons why it is good to go ahead and complete these PQR and WPS requirements from the start, that way you're covered no matter what type of joint comes up.
A way around that, if you so choose, is to take exception to handrails being constructed according to D1.1 in the initial contract. You can state that the handrails are instead constructed according to OSHA Standard CFR, 1926.1052 (c). They meat of this is part (5) which states
"Handrails and the toprails of stairrail systems shall be capable of withstanding, without failure, a force of at least 200 lbs applied within 2 inches of the top edge, in any downward or outward direction, at any point along the top edge."
This way, you can have your engineer design the joints and the weld sizes accordingly to fit your existing or prequalified welding procedures.
Tim