TBH if you are walking up from Keswick via Latrigg, it would not stop you going up via Skiddaw House and down by the tourist route or vice versa since both routes start in the same place past Latrigg. There are other routes too from the car park at the base of the tourist route, e.g. Up the flank of Lonscale Fell, across to Little Man, Skiddaw and down by the tourist trail. The tourist route up can be a bit of a plod and it would be good to vary it into a circular or figure of 8 if you can.
Spikes are easy to acquire especially in Keswick and would be an asset if you are thinking of doing winter trips, they are also on sale at present in a lot of outdoor shops not to mention Amazon. Personally, I would not dream of going up without poles either since they can help you recover from a nasty slip and give added support. If the conditions permit you can go without spikes and poles but please double check the weather and remember if it has been wet, and when isn't it in Cumbria at that time of year, then an overnight freeze could mean ice on paths even if there is no evidence of snow. Water likes to use footpaths as much as we do.