Welcome to the site! Here is information on current conditions from
http://www.shastaavalanche.orgAvalanche Gulch– John Muir Route (Regular Route) via Bunny Flat Trailhead: The avalanche gulch route is hosting poor climbing conditions with deteriorating snow and high rock fall potential. If choosing to climb this route, check the weather, and be prepared. Snow is now patchy from Helen Lake to the Summit Plateau. Be advised that the summer trail to Helen Lake via Horse Camp is fully melted out. At upper 50/50 Flat the trail traverses to the right and ascends moraines to arrive at Helen Lakes right flank. Please use this trail for any summit attempts. There are plenty of existing rock tent platforms as well as snow sites still available at Helen Lake for camping. Don't underestimate the power of wind as you leave your camp to climb. Stake your tent down WELL, and keep gear tidy and tucked away. Animals have been known to tear food sacks apart and make a mess. Rangers often collect abandoned gear and camp trash on the mountain, so please keep a tidy camp! Continuous snow no longer exists climbing right of the Heart. Climbing the normal route requires almost all scree scrambling. Be advised that rockfall on and around this route is increasing, especially as the sun warms the route throughout the day. WEAR A HELMET! This simple tool of noggin protection can prevent a lot of bodily injury and potentially save your life. Further, an ICE AXE and CRAMPONS are recommended for travel on snow, and its up to you to know how to use them. The Redbanks are still passable, though there is no snow remaining through the chutes. Either travel through the notch (top of ridge if on far right side of RB) or go completely climbers left around RB (left of The Heart) but it does get steep (45+ degrees) near the topout at the left side of the RB. The bergschrund at the top of the Konwakition Glacier is open and exposed and travel around the climber's right side of the Redbanks (the thumb route) crossing the top of the glacier is NOT recommended. Misery hill is free of snow and climbers should use the scree trail to ascend. One may descend the same way, but glissading is not possible due to lack of snow. Pay attention to the weather as you climb. Many climbers become lost or disoriented on the upper mountain in the event of incoming weather. Wandering off the wrong side of the mountain has happened to many and is guaranteed to compromise one's safety and time line!
I haven't been to Shasta since mid-August and that was on the north side. From what I have seen though I suspect you can pretty easily find your way up AG without crampons but there may be some areas, maybe 1-2 thousand feet worth at most, where they could be used to bypass the talus.
Another option is Wintun Ridge, which would be snow and crampon free but is more solid and less subject to rockfall. Anything else and you are dealing with rocky ridges, ice (HB ridge) or glaciers I would think.
Sargents Ridge is really not bad in these sorts of conditions, if you don't mind talus, but it is solid class 3, or 4 if you choose, in areas between Shastarama Pt and Thumb Rock.