Hello and welcome to Eve.
Yes, declining all security encounter missions towards the 4 main Empire Factions will help negate incurring negative Faction standings.
Course since you’ve already completed missions for one set of Career Agents, you can also complete all of the Career Agents for each of the 4 main Empire Factions to basically give you equal standings with the 4 main Empire Factions when completed.
However since random Storyline missions are offered after completing 16 missions of the same level for the same Faction, your standings will become lopsided due to different Storyline missions giving varying amounts of positive standing increase and derived negative standing hits. One way to maintain equal standing with all 4 main Empire Factions is to decline those Storyline mission offers.
Another way to maintain equal standings is to rotate completing 16 missions plus Storyline for each of the 4 main Empire Factions. As stated before, Storyline mission offers are random and each give different amounts of positive standing increase as well as incur derived negative standing hits so you’ll have to keep watch on your standings and bounce back and forth between the 4 main Empire Factions as needed.
The 4 main Empire Factions are split up into 2 allied groups, Amarr and Caldari are allied while Minmatar and Gallente are allied. On the flip side of that Amarr and Minmatar are mortal enemy’s along with Caldari and Gallente being mortal enemy’s as well. When standing increase is gained with one Faction, derived negative standing hits is incurred with it’s enemy.
An easy way to explain that is this: You gain 100% positive standing increase with Amarr for completing a Storyline mission offer. At the same time you also incur 50% derived negative standing hit with Amarr’s enemy, the Minmatar. Along with that you also gain 50% positive standing increase with Amarr’s ally, the Caldari and also incur 25% derived negative standing hit with Caldari’s enemy, the Gallente.
To help offset and equalize Faction standings, you can complete Epic Arcs every 90 days. They give large positive standing increase with little to no derived negative standing hits. The Level 1 Sisters Of Eve Epic Arc is great to help equalize Faction standings since it virtually requires very little standing to access and gives you a choice between the 4 main Empire Factions for completion.
Naturally there’s a lot more info pertaining to missions and standings than this brief overview I posted… I hope you have good luck and much success here in Eve.